Poisson <i>C</i>*-algebra derivations in Poisson <i>C</i>*-algebras

Abstract

In this study, we introduce the following additive functional equation: g ( lambda u + v + 2 y ) = lambda g ( u ) + g ( v ) + 2 g ( y ) g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all lambda is an element of C \lambda \in {\mathbb{C}} , all unitary elements u , v u,v in a unital Poisson C * {C}<^>{* } -algebra P P , and all y is an element of P y\in P . Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C * {C}<^>{* } -algebras. Furthermore, we apply to study Poisson C * {C}<^>{* } -algebra homomorphisms and Poisson C * {C}<^>{* } -algebra derivations in unital Poisson C * {C}<^>{* } -algebras.

In this study, we introduce the following additive functional equation: g(λu + v + 2y) = λg(u) + g(v) + 2g(y) for all λ ∈ C, all unitary elements u, v in a unital Poisson C*-algebra P, and all y ∈ P.Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C*-algebras.Furthermore, we apply to study Poisson C*-algebra homomorphisms and Poisson C*-algebra derivations in unital Poisson C*-algebras.