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
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
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 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
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.
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 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）.
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.
