We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan d...We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Bana...Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.展开更多
Let R_1 and R_2 be two rings with unit I. We give some characterizations of ring homomorphisms and ring isomorphisms between R_1 and R_2 in term of complete preservers of fixed points of multipliers, under some mild a...Let R_1 and R_2 be two rings with unit I. We give some characterizations of ring homomorphisms and ring isomorphisms between R_1 and R_2 in term of complete preservers of fixed points of multipliers, under some mild assumption on R_1. Applications to several kinds of operator algebras such as Banach algebras, nest algebras, matrix algebras and standard operator algebras are presented.展开更多
Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positiv...Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).展开更多
In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particul...In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.展开更多
In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach ...In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.展开更多
We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein ...We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.展开更多
Let N and M be nests on Banach spaces X and Y over the real or complex field F, respectively, with the property that if M ∈ M such that M_ =M, then M is complemented in Y. Let AlgN and AlgM be the associated nest alg...Let N and M be nests on Banach spaces X and Y over the real or complex field F, respectively, with the property that if M ∈ M such that M_ =M, then M is complemented in Y. Let AlgN and AlgM be the associated nest algebras. Assume that Ф ： AlgN → AlgM is a bijective map. It is proved that, if dim X = ∞ and if there is a nontrivial element in N which is complemented in X, then Ф is Lie multiplicative （i.e. Ф（[A, B]） = [Ф（A）, Ф（B）] for all A, B ∈ AlgN） if and only if Ф has the form Ф（A） = TAT^-1 ＋ τ（A） for all A ∈ AlgAN or Ф（A） = -TA^＊T^-1 ＋ τ（A） for all A ∈ AlgN, where T is an invertible linear or conjugate linear operator and τ ： AlgN →FI is a map with τ（[A, B]） = 0 for all A, B ∈ AlgN. The Lie multiplicative maps are also characterized for the case dim X 〈 ∞.展开更多
In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give ...In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.展开更多
Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved ...Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved that, if E_m(R) is isomorphic to E_n(A) then m=n (cf. Ref. [1]). When n≥4, every isomorphism E_n(R)E_n(A) is of the standard type, and it can be naturally and uniquely lifted to an isomorphism from St_n(R) to St_n(A) (cf. Refs. [1] and [2]). However, the case n=3 is different from that n≥4,展开更多
Metal oxides as support for constructing precious metal single-atom catalysts hold great promise for a wide range of industrial applications,but achieving a high-loading of thermally stable metal single atoms on such ...Metal oxides as support for constructing precious metal single-atom catalysts hold great promise for a wide range of industrial applications,but achieving a high-loading of thermally stable metal single atoms on such supports has been challenging.Herein,we report an innovative strategy for the fabrication of high-density single-atoms(Rh,Ru,Pd)catalysts on CaAl-layered double hydroxides(CaAl-LDH)via isomorphous substitution.The Rh species have occupied Ca^(2+)vacancies within CaAl-LDH laminate by ion-exchange,facilitating a substantial loading of isolated Rh single-atoms.Such catalysts displayed superior performance in the selective hydrogenation to quinoline,pivotal for liquid organic hydrogen storage,and the universality for the hydrogenation of N-heterocyclic aromatic hydrocarbons was also verified.Combining the experimental results and density functional theory calculations,the pathway of quinoline hydrogenation over Rh1CaAl-LDH was proposed.This synthetic strategy marks a significant advancement in the field of single-atom catalysts,expanding their horizons in green chemical processes.展开更多
1. Introduction Since O’Meara worked out the automorphisms of orthogonal groups Ωn(V) over fields in [4] by using well-known residual space method, many results about the isomorphisms and automorphisms of orthogonal...1. Introduction Since O’Meara worked out the automorphisms of orthogonal groups Ωn(V) over fields in [4] by using well-known residual space method, many results about the isomorphisms and automorphisms of orthogonal groups over integral domains have been achieved. Refer to O’Meara, Hahn for example. B. R. McDonald, in [12], determined the automorphisms of O(V) over local rings with 2 a unit by using involutions.展开更多
In this paper, we discuss the necessary and sufficient conditions in which there exist exceptional isomorphisms between E3（A） and E3（R） and between GL3（A） and GL3（R） for commutative rings A and R. A counterexa...In this paper, we discuss the necessary and sufficient conditions in which there exist exceptional isomorphisms between E3（A） and E3（R） and between GL3（A） and GL3（R） for commutative rings A and R. A counterexample shows that two rings that are not isomorphic may have isomorphic tinear groups. This partly solves an open problem posed at the conference on abstract homomorphisms of algebraic groupsrs.展开更多
Isomorphic substitution of ferric ion(Fe~(3+))by aluminum ion(Al~(3+))in iron(hydro)oxides is ubiquitous in natural environments.Aluminum substitution inevitably leads to changes in the microstructures,physicochemical...Isomorphic substitution of ferric ion(Fe~(3+))by aluminum ion(Al~(3+))in iron(hydro)oxides is ubiquitous in natural environments.Aluminum substitution inevitably leads to changes in the microstructures,physicochemical properties,and surface reactions of iron(hydro)oxides,which may have great impacts on the sequestration of nutrients and contaminants in soils and aquatic environments.Over the past decades,the structural properties and surface reactivity of Al-substituted iron(hydro)oxides have been intensively studied.Iron(hydro)oxides in various structural forms and with different Al substitution amounts present high application potentials in addressing environmental issues.A timely summary of the structural properties and interfacial reactions of the most common and representative Al-substituted iron(hydro)oxides is of significance.Herein,the effects of Al substitution on the structural properties and surface activities of iron(hydro)oxides were clarified according to the microstructure,crystal facets,surface site type and density,interfacial reaction mechanisms,and modeling parameters of iron(hydro)oxides.This review systematically elucidates how Al substitution affects the structural properties and surface reactions of iron(hydro)oxides,including the well crystallized goethite and hematite and the poorly crystallized ferrihydrite,providing theoretical guidance for further exploration of the mineralogical characteristics and environmental geochemical behaviors of iron(hydro)oxides.展开更多
In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert sp...In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator.In this work,we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.By utilizing the Choi-Jamio lkowski isomorphism,we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian.Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence.Moreover,to address scenarios with degenerate steady states,we introduce an iterative energy-offset scanning technique.Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths.These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.展开更多
Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I....Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.展开更多
By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it...By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.展开更多
In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application o...In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.展开更多
By considering the Galois action and the group action,we give the relation of two isomorphism character rings on the arbitrary field K with CharK = 0.Our results generalize Saksonov's theorem.
文摘We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
文摘Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.
基金Supported by the National Natural Science Foundation of China(Grant No.11671294)
文摘Let R_1 and R_2 be two rings with unit I. We give some characterizations of ring homomorphisms and ring isomorphisms between R_1 and R_2 in term of complete preservers of fixed points of multipliers, under some mild assumption on R_1. Applications to several kinds of operator algebras such as Banach algebras, nest algebras, matrix algebras and standard operator algebras are presented.
基金supported by the National Natural Science Foundation of China(11801555 and 11971058)the Fundamental Research Funds for the Central Universities(2020YQLX02)supported by the National Natural Science Foundation of China(11971058,11761131002 and 11671185)。
文摘Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).
基金Supported by the National Natural Science Foundation of China.
文摘In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.
文摘In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.
基金supported by National Natural Science Foundation of China(Grant Nos.12061060 and 11801141)Scientific and Technological Planning Project of Yunnan Province(Grant No.202305AC160005)Scientific and Technological Innovation Team of Yunnan Province(Grant No.2020CXTD25)。
文摘We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.
基金supported by National Natural Science Foundation of China (Grant No. 10871111)Tian Yuan Foundation of China (Grant No. 11026161)Foundation of Shanxi University
文摘Let N and M be nests on Banach spaces X and Y over the real or complex field F, respectively, with the property that if M ∈ M such that M_ =M, then M is complemented in Y. Let AlgN and AlgM be the associated nest algebras. Assume that Ф ： AlgN → AlgM is a bijective map. It is proved that, if dim X = ∞ and if there is a nontrivial element in N which is complemented in X, then Ф is Lie multiplicative （i.e. Ф（[A, B]） = [Ф（A）, Ф（B）] for all A, B ∈ AlgN） if and only if Ф has the form Ф（A） = TAT^-1 ＋ τ（A） for all A ∈ AlgAN or Ф（A） = -TA^＊T^-1 ＋ τ（A） for all A ∈ AlgN, where T is an invertible linear or conjugate linear operator and τ ： AlgN →FI is a map with τ（[A, B]） = 0 for all A, B ∈ AlgN. The Lie multiplicative maps are also characterized for the case dim X 〈 ∞.
文摘In this paper we give the following main results: (ⅰ) Let F(?) and G(?) be two free modules. Then F(?) and G(?) are semi-linearly isomorphic if and only if End F(?) and End G(?) are strictly isomorphic. (ⅱ) We give a new method to generalize the Bolla theorem in 1985 which gave a categorical description for isomorphism between End F(?) and End G(?). (ⅲ) The Wolfson theorem is a corollary of our theorem.
基金Project supported by the National Natural Science Foundation of China
文摘Let R and A be commutative rings with identity, and m and n be integers ≥3. Consider when and how an isomorphism E_m(R)E_n(A) can be lifted to an isomorphism between the corresponding Steinberg groups. It was proved that, if E_m(R) is isomorphic to E_n(A) then m=n (cf. Ref. [1]). When n≥4, every isomorphism E_n(R)E_n(A) is of the standard type, and it can be naturally and uniquely lifted to an isomorphism from St_n(R) to St_n(A) (cf. Refs. [1] and [2]). However, the case n=3 is different from that n≥4,
文摘Metal oxides as support for constructing precious metal single-atom catalysts hold great promise for a wide range of industrial applications,but achieving a high-loading of thermally stable metal single atoms on such supports has been challenging.Herein,we report an innovative strategy for the fabrication of high-density single-atoms(Rh,Ru,Pd)catalysts on CaAl-layered double hydroxides(CaAl-LDH)via isomorphous substitution.The Rh species have occupied Ca^(2+)vacancies within CaAl-LDH laminate by ion-exchange,facilitating a substantial loading of isolated Rh single-atoms.Such catalysts displayed superior performance in the selective hydrogenation to quinoline,pivotal for liquid organic hydrogen storage,and the universality for the hydrogenation of N-heterocyclic aromatic hydrocarbons was also verified.Combining the experimental results and density functional theory calculations,the pathway of quinoline hydrogenation over Rh1CaAl-LDH was proposed.This synthetic strategy marks a significant advancement in the field of single-atom catalysts,expanding their horizons in green chemical processes.
文摘1. Introduction Since O’Meara worked out the automorphisms of orthogonal groups Ωn(V) over fields in [4] by using well-known residual space method, many results about the isomorphisms and automorphisms of orthogonal groups over integral domains have been achieved. Refer to O’Meara, Hahn for example. B. R. McDonald, in [12], determined the automorphisms of O(V) over local rings with 2 a unit by using involutions.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, we discuss the necessary and sufficient conditions in which there exist exceptional isomorphisms between E3（A） and E3（R） and between GL3（A） and GL3（R） for commutative rings A and R. A counterexample shows that two rings that are not isomorphic may have isomorphic tinear groups. This partly solves an open problem posed at the conference on abstract homomorphisms of algebraic groupsrs.
基金financially supported by the National Natural Science Foundation of China(Nos.42207352,42007020,and 42007015)the Natural Science Fund for Excellent Young Scholars of Hainan Province,China(No.324YXQN421)。
文摘Isomorphic substitution of ferric ion(Fe~(3+))by aluminum ion(Al~(3+))in iron(hydro)oxides is ubiquitous in natural environments.Aluminum substitution inevitably leads to changes in the microstructures,physicochemical properties,and surface reactions of iron(hydro)oxides,which may have great impacts on the sequestration of nutrients and contaminants in soils and aquatic environments.Over the past decades,the structural properties and surface reactivity of Al-substituted iron(hydro)oxides have been intensively studied.Iron(hydro)oxides in various structural forms and with different Al substitution amounts present high application potentials in addressing environmental issues.A timely summary of the structural properties and interfacial reactions of the most common and representative Al-substituted iron(hydro)oxides is of significance.Herein,the effects of Al substitution on the structural properties and surface activities of iron(hydro)oxides were clarified according to the microstructure,crystal facets,surface site type and density,interfacial reaction mechanisms,and modeling parameters of iron(hydro)oxides.This review systematically elucidates how Al substitution affects the structural properties and surface reactions of iron(hydro)oxides,including the well crystallized goethite and hematite and the poorly crystallized ferrihydrite,providing theoretical guidance for further exploration of the mineralogical characteristics and environmental geochemical behaviors of iron(hydro)oxides.
基金supported by the National Natural Science Foundation of China(Grant Nos.12375013 and 12275090)the Guangdong Basic and Applied Basic Research Fund(Grant No.2023A1515011460)Guangdong Provincial Quantum Science Strategic Initiative(Grant No.GDZX2200001)。
文摘In open quantum systems,the Liouvillian gap characterizes the relaxation time toward the steady state.However,accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator.In this work,we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap.By utilizing the Choi-Jamio lkowski isomorphism,we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian.Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence.Moreover,to address scenarios with degenerate steady states,we introduce an iterative energy-offset scanning technique.Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths.These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.
文摘Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.
基金Supported by the National Natural Science Foundation of China (Grant No. 10471114)
文摘By a ball-covering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.
文摘In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS)algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inner. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.
文摘By considering the Galois action and the group action,we give the relation of two isomorphism character rings on the arbitrary field K with CharK = 0.Our results generalize Saksonov's theorem.
