Approximately linear mappings in banach modules over a C*-algebra
- Authors
- Park, Choonkil; Jian Lian Cui
- Issue Date
- Nov-2007
- Publisher
- SPRINGER HEIDELBERG
- Keywords
- C*-algebra homomorphism; Poisson Banach module over Poisson C*-algebra; Poisson C *-algebra homomorphism; Poisson JC*-algebra homomorphism; Stability
- Citation
- ACTA MATHEMATICA SINICA-ENGLISH SERIES, v.23, no.11, pp.1919 - 1936
- Indexed
- SCIE
SCOPUS
- Journal Title
- ACTA MATHEMATICA SINICA-ENGLISH SERIES
- Volume
- 23
- Number
- 11
- Start Page
- 1919
- End Page
- 1936
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/172217
- DOI
- 10.1007/s10114-007-0964-2
- ISSN
- 1439-8516
- Abstract
- Let X and Y be vector spaces. The authors show that a mapping f: X -> Y satisfies the functional equation [GRAPHICS] with f(0) = 0 if and only if the mapping f: X -> Y is Cauchy additive, and prove the stability of the functional equation (double dagger) 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 B is a homomorphism when h((2d-1)(n)uy) = h((2d-1)(n)u)h(y) or h((2d-1)(n)u.y) = h((2d-1)(n)u).h(y) for all unitaries u is an element of A, all y is an element of A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.
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