Hyers–Ulam–Rassias stability of a generalized Apollonius–Jensen type additive mapping and isomorphisms between C *‐algebras |
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Authors: | Choonkil Park |
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Institution: | Department of Mathematics, Hanyang University, Seoul, 133–791, Republic of Korea |
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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: 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 . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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Keywords: | Hyers− Ulam− Rassias stability generalized Apollonius− Jensen type additive mapping isomorphism between C *‐algebras |
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