Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach

Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach

Year:    2011

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 4 : pp. 320–331

Abstract

Let $A$, $B$ be two unital $C^*$−algebras. By using fixed point methods, we prove that every almost unital almost linear mapping $h : A \to B$ which satisfies $h(2^nuy)= h(2^nu)h(y)$ for all $u \in U(A)$, all $y \in A$, and all $n=0,1,2, \cdots$, is a homomorphism. Also, we establish the generalized Hyers–Ulam–Rassias stability of $*$−homomorphisms on unital $C^*$−algebras.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.1007/s10496-011-0320-3

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 4 : pp. 320–331

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    alternative fixed point Jordan $*$-homomorphism.