Poisson Banach Modules over a Poisson C*-Algebr

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 4,  2008, pp.529-543
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.4.529
Title & Authors
Poisson Banach Modules over a Poisson C*-Algebr
Park, Choon-Kil;

Abstract
It is shown that every almost linear mapping h : $\small{A{\rightarrow}B}$ of a unital PoissonC*-algebra A to a unital Poisson C*-algebra B is a Poisson C*-algebra homomorph when $\small{h(2^nuy)\;=\;h(2^nu)h(y)}$ or $\small{h(3^nuy)\;=\;h(3^nu)h(y)}$ for all $\small{y\;\in\;A}$, all unitary elements $\small{u\;\in\;A}$ and n = 0, 1, 2,$\small{\codts}$, and that every almost linear almost multiplicative mapping h : $\small{A{\rightarrow}B}$ is a Poisson C*-algebra homomorphism when h(2x) = 2h(x) or h(3x) = 3h(x for all $\small{x\;\in\;A}$. Here the numbers 2, 3 depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings. We prove the Cauchy-Rassias stability of Poisson C*-algebra homomorphisms in unital Poisson C*-algebras, and of homomorphisms in Poisson Banach modules over a unital Poisson C*-algebra.
Keywords
Poisson C*-algebra homomorphism;Poisson Banach module;Poisson C*-algebra;stability;linear functional equation;
Language
English
Cited by
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