Left or right centralizers on $ \star $-algebras through orthogonal elements

TL;DR

This paper investigates linear maps on special $\star$-algebras that act like left or right centralizers at orthogonal elements, providing new characterizations of such maps.

Contribution

It offers novel characterizations of linear maps behaving as centralizers at orthogonal elements in special $\star$-algebras.

Findings

Characterization of linear maps acting as centralizers at orthogonal elements

Results applicable to special $\star$-algebras

Insights into the structure of such linear maps

Abstract

In this paper we consider the problem of characterizing linear maps on special $ \star $-algebras behaving like left or right centralizers at orthogonal elements and obtain some results in this regard.