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- W1966774110 abstract "Abstract. It is shown that every almost linear mapping h: A → B of a unital PoissonC ∗ -algebra A to a unital Poisson C ∗ -algebra B is a Poisson C -algebra homomorphismwhen h(2 n uy) = h(2 n u)h(y) or h(3 n uy) = h(3 n u)h(y) for all y∈ A, all unitary elementsu∈ A and n= 0,1,2,···, and that every almost linear almost multiplicative mappingh: A → B is a Poisson C ∗ -algebra homomorphism when h(2x) = 2h(x) or h(3x) = 3h(x)for all x∈ A. Here the numbers 2,3 depend on the functional equations given in thealmost linear mappings or in the almost linear almost multiplicative mappings. We provethe 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. 1. IntroductionA Poisson C ∗ -algebra A is a C ∗ -algebra with a C-bilinear map {·,·} : A×A →A, called a Poisson bracket, such that (A,{·,·}) is a complex Lie algebra and{ab,c} = a{b,c}+{a,c}bfor all a,b,c ∈ A. Poisson algebras have played an important role in many mathe-matical areas and have been studied to find sympletic leaves of the correspondingPoisson varieties. It is also important to find or construct a Poisson bracket in thetheory of Poisson algebra.A Poisson Banach module X over a Poisson C" @default.
- W1966774110 created "2016-06-24" @default.
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- W1966774110 date "2008-12-31" @default.
- W1966774110 modified "2023-09-26" @default.
- W1966774110 title "Poisson Banach Modules over a Poisson C*-Algebr" @default.
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- W1966774110 doi "https://doi.org/10.5666/kmj.2008.48.4.529" @default.
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