Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to...Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to B is a nonzero scalar multiple of either a linear＊-isomorphism or a conjugate linear ＊-isomorphism.展开更多
We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)...We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)→vM with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic(as a Banach space) to B(l2). For instance this applies(rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property(due to Szankowski) there are M ’s(namely B(H)^(**) and certain finite examples defined using ultraproducts) that are not seemingly injective.Moreover, for M to be seemingly injective it suffices to have the above factorization of I dM through B(H) with u, v positive(and u still normal).展开更多
In this paper,we prove that if a bijective mapΦpreserves mixed Jordan triple products between von Neumann algebras with no central abelian projections,thenΦ(I)Φis the sum of a linear*-isomorphism and a conjugate li...In this paper,we prove that if a bijective mapΦpreserves mixed Jordan triple products between von Neumann algebras with no central abelian projections,thenΦ(I)Φis the sum of a linear*-isomorphism and a conjugate linear*-isomorphism,whereΦ(I)is a self-adjoint central element in the range withΦ(I)^(2)=I.Also,we give the structure of this map that preserves mixed Jordan triple products between factor von Neumann algebras.展开更多
Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of...Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of this article is to introduce generalized weak wave operators Wf_(±),generalized weak abelian wave operators ■ and generalized stationary wave operators U_(±) in M and then to explore the relation among W_(±),■,U_(±) and generalized wave operators W_(±).展开更多
In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A...In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.展开更多
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
It is proved that everyσ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A(or B)is a derivation.Morevoer,if A is also aσ-Dirichlet subalgebra,each local deri...It is proved that everyσ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A(or B)is a derivation.Morevoer,if A is also aσ-Dirichlet subalgebra,each local derivation from A into A is an inner derivation.展开更多
In this paper,we introduce Frobenius von Neumann algebras and study quantum convolution inequalities.In this framework,we unify quantum Young's inequality on quantum symmetries such as subfactors,and fusion bi-alg...In this paper,we introduce Frobenius von Neumann algebras and study quantum convolution inequalities.In this framework,we unify quantum Young's inequality on quantum symmetries such as subfactors,and fusion bi-algebras studied in quantum Fourier analysis.Moreover,we prove quantum entropic convolution inequalities and characterize the extremizers in the subfactor case.We also prove quantum smooth entropic convolution inequalities.We obtain the positivity of comultiplications of subfactor planar algebras,which is stronger than the quantum Schur product theorem.All these inequalities provide analytic obstructions of unitary categorification of fusion rings stronger than the Schur product criterion.展开更多
Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) =...Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.展开更多
Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A wi...Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A.展开更多
In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanis...In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.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
In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve ...In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.展开更多
We show that every local 3-cocycle of a von Neumann algebra $\mathcal{R}$ into an arbitrary unital dual $\mathcal{R}$ -bimodule $\mathcal{S}$ is a 3-cocycle.
Let M and N be the yon Neumann algebras induced by the rational action of the group SL2（R） and its subgroup P on the upper half plane H. We have shown that N is spatial isomorphic to the group von Neumann algebra L...Let M and N be the yon Neumann algebras induced by the rational action of the group SL2（R） and its subgroup P on the upper half plane H. We have shown that N is spatial isomorphic to the group von Neumann algebra Lp and characterized M and its commutant M＇ and gotten a generalization of the Mautner＇s lemma. It is also shown that the Berezin operator commutates with the Laplaeian operator.展开更多
Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension...Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension. We show that this invariant is independent of the generating set, and we extend results in Hadwin-Shen (2007) to this larger class of algebras.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11501401)
文摘Let H, K be infinite dimensional complex Hilbert spaces, and A, B be factor von Neumann algebras on H and K, respectively. It is shown that every surjective map completely preserving Jordan 1-＊-zero-product from A to B is a nonzero scalar multiple of either a linear＊-isomorphism or a conjugate linear ＊-isomorphism.
文摘We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of Id_(M)= vu : M→uB(H)→vM with u normal, unital, positive and v completely contractive. As a corollary, if M has a separable predual, M is isomorphic(as a Banach space) to B(l2). For instance this applies(rather surprisingly) to the von Neumann algebra of any free group. Nevertheless, since B(H) fails the approximation property(due to Szankowski) there are M ’s(namely B(H)^(**) and certain finite examples defined using ultraproducts) that are not seemingly injective.Moreover, for M to be seemingly injective it suffices to have the above factorization of I dM through B(H) with u, v positive(and u still normal).
基金Supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2018BA003)the National Natural Science Foundation of China(Grant No.11801333)。
文摘In this paper,we prove that if a bijective mapΦpreserves mixed Jordan triple products between von Neumann algebras with no central abelian projections,thenΦ(I)Φis the sum of a linear*-isomorphism and a conjugate linear*-isomorphism,whereΦ(I)is a self-adjoint central element in the range withΦ(I)^(2)=I.Also,we give the structure of this map that preserves mixed Jordan triple products between factor von Neumann algebras.
基金Supported by the Undergraduate Training Program on Innovation and Entrepreneurship(Grant No.X202110251333)National Natural Science Foundation of China(Grant No.11671133).
文摘Let M⊆B(H)be a countable decomposable properly infinite von Neumann algebra with a faithful normal semifinite tracial weightτwhere B(H)is the set of all bounded linear operators on Hilbert space H.The main purpose of this article is to introduce generalized weak wave operators Wf_(±),generalized weak abelian wave operators ■ and generalized stationary wave operators U_(±) in M and then to explore the relation among W_(±),■,U_(±) and generalized wave operators W_(±).
基金The National Science Foundation (99A019, 2002X10) of the Education Committee of Hubei Province.
文摘In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of a von Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
文摘It is proved that everyσ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A(or B)is a derivation.Morevoer,if A is also aσ-Dirichlet subalgebra,each local derivation from A into A is an inner derivation.
基金supported by Beijing Municipal Science&Technology Commission,Administrative Commission of Zhongguancun Science Park(Grant No.Z221100002722017)supported by grants from Beijing Institute of Mathematical Sciences and Applications+4 种基金supported by China’s National Key R&D Programmes(Grant No.2020YFA0713000)Tsinghua University(Grant No.04200100122)Templeton Religion Trust(TRT 159)supported by Beijing Natural Science Foundation Key Program(Grant No.Z220002)supported by National Natural Science Foundation of China(Grant Nos.12031004 and 12371124)。
文摘In this paper,we introduce Frobenius von Neumann algebras and study quantum convolution inequalities.In this framework,we unify quantum Young's inequality on quantum symmetries such as subfactors,and fusion bi-algebras studied in quantum Fourier analysis.Moreover,we prove quantum entropic convolution inequalities and characterize the extremizers in the subfactor case.We also prove quantum smooth entropic convolution inequalities.We obtain the positivity of comultiplications of subfactor planar algebras,which is stronger than the quantum Schur product theorem.All these inequalities provide analytic obstructions of unitary categorification of fusion rings stronger than the Schur product criterion.
基金supported by the National Natural Science Foundation of China(No.11526123,No.11401273)the Natural Science Foundation of Shandong Province of China(No.ZR2015PA010)
文摘Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.
基金supported by the National Natural Science Foundation of China(No.11401452)the China Postdoctoral Science Foundation(No.2015M581513)
文摘Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A.
基金The first author is supported by Natural Science Foundation of Shandong Province,China(Grant No.ZR2015PA010)National.Natural Science Foundation of China(GrantNo.11526123)The third author is supported by the National Natural Science Foundation of China(Grant No.11401273).
文摘In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.
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 Chinese Universities Scientific Fund(Grant No.WK0010000031)supported by National Natural Science Foundation of China(Grant Nos.11231390,11371222,11301511)
文摘In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.
基金This work was partially supported by the National Natural Science Foundation of China (Grant Nos.10201007 and A0324614)the Natural Science Foundation of Shandong Province (Grant No.Y2006A03)
文摘We show that every local 3-cocycle of a von Neumann algebra $\mathcal{R}$ into an arbitrary unital dual $\mathcal{R}$ -bimodule $\mathcal{S}$ is a 3-cocycle.
基金Supported by National Natural Science Foundation of China （Grant No. 10871111） and Chongqing Municipal Education Commission （Grant No. KJ090804） and Chongqing Normal University （Grant No. 08XLB013）
文摘Let M and N be the yon Neumann algebras induced by the rational action of the group SL2（R） and its subgroup P on the upper half plane H. We have shown that N is spatial isomorphic to the group von Neumann algebra Lp and characterized M and its commutant M＇ and gotten a generalization of the Mautner＇s lemma. It is also shown that the Berezin operator commutates with the Laplaeian operator.
基金Supported by the Zhejiang Qianjiang Talent Program in 2008the Program for New Century Excellent Talents in University of Ministry of Education of China in 2010+1 种基金the National Natural Science Foundation of China(Grant No.11271321)the Fundamental Research Funds of Zhejiang University
文摘In this note, we show that avon Neumann algebra M is injective if and only if the weak＊ similarity degree d.（M） ≤ 2.
文摘Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension. We show that this invariant is independent of the generating set, and we extend results in Hadwin-Shen (2007) to this larger class of algebras.
