Hyers-Ulam-Rassias stability of a generalized Apollonius-Jensen type additive mapping and isomorphisms between C*-algebras
- Authors
- Park, Choonkil
- Issue Date
- Feb-2008
- Publisher
- WILEY-V C H VERLAG GMBH
- Keywords
- Hyers-Ulam-Rassias stability; generalized Apollonius-Jensen type additive mapping; isomorphism between C*-algebras
- Citation
- MATHEMATISCHE NACHRICHTEN, v.281, no.3, pp.402 - 411
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATISCHE NACHRICHTEN
- Volume
- 281
- Number
- 3
- Start Page
- 402
- End Page
- 411
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/178979
- DOI
- 10.1002/mana.200510611
- ISSN
- 0025-584X
- Abstract
- Let X, Y be Banach modules over a C *-algebra. We prove the Hyers–Ulam–Rassias stability of the following functional equation in Banach modules over a unital C *-algebra: equation image
It is shown that a mapping f: X → Y satisfies the above functional equation and f (0) = 0 if and only if the mapping f: X → Y is Cauchy additive. As an application, we show that every almost linear bijection h: A → B of a unital C *-algebra A onto a unital C *-algebra B is a C *-algebra isomorphism when h (2d uy) = h (2d u) h (y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z.
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