Characterization of Jordan homomorphisms and Jordan derivations

Document Type : Original Article

Author

Abbas Zivari-Kazempour

Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran

10.22034/kjm.2023.385509.2768

Abstract

‎We show that if $f:A\longrightarrow B$ is a continuous linear map between Banach algebras satisfying $f(a\circ b)=f(a)\circ f(b)$ for all $a,b\in A$ with $a\circ b=e_A$ or $ab=ba=e_A$‎, ‎then $f$ is a Jordan homomorphism‎. ‎It is also proved that if $\delta:A\longrightarrow X$ is a continuous linear map satisfying $\delta(a\circ b)=\delta(a)b+a\delta(b)$ for all $a,b\in A$ with $a\circ b=w$‎, ‎where $w\in Z(A)$ is a right (or left) separating point of Banach $A$-bimodule $X$‎, ‎then $\delta$ is a generalized Jordan derivation‎.
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Keywords

Jordan homomorphism‎

‎[generalized] Jordan derivation‎

‎separating point

Subjects

• 47 Operator theory

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