Characterizing derivations and anti-derivations on group algebras through orthogonality

TL;DR

This paper characterizes derivations and anti-derivations on group algebras and measure algebras of locally compact groups by examining their behavior at orthogonal elements under various orthogonality conditions.

Contribution

It provides a new characterization of derivations and anti-derivations on group algebras based on orthogonality conditions, extending understanding of their structure.

Findings

Characterization of derivations via orthogonality conditions

Extension of derivation concepts to anti-derivations

Applicable to various types of orthogonality conditions

Abstract

Let L^1(G) and M(G) be group algebra and measure algebra of a locally compact group G, respectively and D:L^1(G)-->M(G) be a continuous linear map. We consider D behaving like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions and we characterize such maps.