Linear maps preserving identity products

Author
Abbas Zivari-Kazempour
Ayatollah Boroujerdi University
Abstract
Let A and B be two C * -algebras, A is unital and ϕ:A⟶B be a continuous linear map. In this paper, under certain condition, we prove that ϕ is a Jordan * -homomorphism. We also prove that if X is a Banach * -A -bimodule, and σ:A⟶X is a continuous linear map satisfying derivation (Jordan derivation) equation with y * =1 (x∘ y * =1) , then σ is a *-derivation
Keywords
Homomorphism
Jordan homomorphism
Derivation
Jordan derivation
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