K-Commuting Mappings of Generalized Matrix Algebras

TL;DR

This paper characterizes the structure of $k$-commuting mappings in generalized matrix algebras, showing they are proper under mild conditions and extending previous results to a broader algebraic context.

Contribution

It determines the general form of $k$-commuting mappings in generalized matrix algebras and extends existing results to this more general setting.

Findings

$k$-commuting mappings have a specific proper form

Under mild assumptions, all such mappings are properly characterized

The results generalize previous work to broader algebraic structures

Abstract

In this paper we will study $k$-commuting mappings of generalized matrix algebras. The general form of arbitrary $k$-commuting mapping of a generalized matrix algebra is determined. It is shown that under mild assumptions, every $k$-commuting mapping of a generalized matrix algebra takes a certain form which is said to be proper. A number of applications related to $k$-commuting mappings are presented. These results extend the existing works of Cheung, Du and Wang \cite{Cheung2, DuWang1} to the case of generalized matrix