✦ LIBER ✦
Hyers–Ulam–Rassias stability of a generalized Apollonius–Jensen type additive mapping and isomorphisms between C *-algebras
✍ Scribed by Choonkil Park
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 147 KB
- Volume
- 281
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
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 (2^d^ uy) = h (2^d^ u) h (y) for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)