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;
It is shown that every almost linear mapping h : of a unital PoissonC*-algebra A to a unital Poisson C*-algebra B is a Poisson C*-algebra homomorph when or for all , all unitary elements and n = 0, 1, 2,, and that every almost linear almost multiplicative mapping h : is a Poisson C*-algebra homomorphism when h(2x) = 2h(x) or h(3x) = 3h(x for all . 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.