Automorphisms on a C*-algebra and isomorphisms between lie JC*-algebras associated with a generalized additive mapping
- Authors
- Park, Choonkil
- Issue Date
- 2007
- Publisher
- UNIV HOUSTON
- Keywords
- banach module over C*-algebra; Cauchy-Rassias stability; linear functional equation; automorphism on C*-algebra; Lie JC*-algebra isomorphism
- Citation
- HOUSTON JOURNAL OF MATHEMATICS, v.33, no.3, pp.815 - 837
- Indexed
- SCIE
SCOPUS
- Journal Title
- HOUSTON JOURNAL OF MATHEMATICS
- Volume
- 33
- Number
- 3
- Start Page
- 815
- End Page
- 837
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/180615
- ISSN
- 0362-1588
- Abstract
- Let X, Y be vector spaces, and let r be 1 or 3. It is shown that if an odd mapping f : X -> Y satisfies the functional equation [GRAPHICS] then the odd mapping f : X -> Y is additive, and we prove the Cauchy-Rassias stability of the functional equation (0.1) in Banach modules over a unital C*-algebra. As an application, we show that every almost linear bijective mapping h : A -> A on a unital C*-algebra A is an automorphism when h(3(n)uy) = h(3(n)u)h(y) for all unitaries u epsilon A, all y epsilon A and all n epsilon Z, and that every almost linear bijective mapping h : A -> B of a unital Lie JC*-algebra A onto a unital Lie JC*-algebra B is a Lie JC*-algebra isomorphism when h(3(n)u circle y) = h(3(n)u) circle h(y) for all y epsilon A, all unitaries u epsilon A and all n epsilon Z.
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