Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X...Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras.展开更多
In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equatio...In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.展开更多
Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "c...Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "compact" module maps on E. In the case that A isinfinitely dimensional primitive C~*-algebra, E is shown to be self-dual if and only if E isalgebraically finitely generated.展开更多
We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^＊-algebra. The main purpose of this paper is to investigate N-isometric C^＊-algebra isomorphisms between l...We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^＊-algebra. The main purpose of this paper is to investigate N-isometric C^＊-algebra isomorphisms between linear N-normed C^＊-algebras, N-isometric Poisson C^＊-algebra isomorphisms between linear N-normed Poisson C^＊-algebras, N-isometric Lie C^＊-algebra isomorphisms between linear N-normed Lie C^＊-algebras, N-isometric Poisson JC^＊-algebra isomorphisms between linear N-normed Poisson JC^＊-algebras, and N-isometric Lie JC^＊-algebra isomorphisms between linear N-normed Lie JC^＊-algebras. Moreover, we prove the Hyers- Ulam stability of t：heir N-isometric homomorphisms.展开更多
基金Grant No. F01-2006-000-10111-0 from the Korea Science & Engineering FoundationThe second author is supported by National Natural Science Foundation of China (No.10501029)+1 种基金Tsinghua Basic Research Foundation (JCpy2005056)the Specialized Research Fund for Doctoral Program of Higher Education
文摘Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras.
基金supported by Korea Research Foundation Grant KRF-2002-041-C00014
文摘In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.
基金Project partially supported by the National Natural Science Foundation of China.
文摘Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "compact" module maps on E. In the case that A isinfinitely dimensional primitive C~*-algebra, E is shown to be self-dual if and only if E isalgebraically finitely generated.
基金The first author is supported by Korea Research Foundation Grant KRF-2005-041-C00027
文摘We prove the Hyers-Ulam stability of linear N-isometries in linear N-normed Banach mod- ules over a unital C^＊-algebra. The main purpose of this paper is to investigate N-isometric C^＊-algebra isomorphisms between linear N-normed C^＊-algebras, N-isometric Poisson C^＊-algebra isomorphisms between linear N-normed Poisson C^＊-algebras, N-isometric Lie C^＊-algebra isomorphisms between linear N-normed Lie C^＊-algebras, N-isometric Poisson JC^＊-algebra isomorphisms between linear N-normed Poisson JC^＊-algebras, and N-isometric Lie JC^＊-algebra isomorphisms between linear N-normed Lie JC^＊-algebras. Moreover, we prove the Hyers- Ulam stability of t：heir N-isometric homomorphisms.
