International Journal of Nonlinear Analysis and Applications

Maps on Banach *-algebras acting at the identity products

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics‎, Faculty of Basic Sciences, ‎‎Ayatollah Boroujerdi University‎, ‎Boroujerd‎, ‎Iran

Abstract

Let $A$ be a unital Banach $*$-algebra with unit $1$, and $X$ be a Banach $*$-$A$-bimodule. In this paper, we determining continuous linear maps $\delta:A\longrightarrow X$ that satisfy one of the following conditions:
\[\delta(x \diamond y)=\delta(x)\diamond y, \]
\[\delta(x \diamond y \diamond x)=\delta(x)\diamond y \diamond x,\]
for all $x,y\in A$ with $xy=1$, where $x \diamond y=x^*y-y^*x$. We also characterize continuous linear maps $\phi:A\longrightarrow B$ which behave like homomorphisms at the identity products.

Keywords

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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 30 August 2025
  • Receive Date: 31 May 2024
  • Revise Date: 21 January 2025
  • Accept Date: 30 January 2025