On $\theta$-centralizing $\theta$-generalized derivations on convolution algebras

TL;DR

This paper studies a class of generalized derivations on convolution algebras, showing they are equivalent to certain centralizers under specific conditions, thus advancing understanding of algebraic structures in functional analysis.

Contribution

It establishes that all $ heta$-centralizing and $ heta$-skew centralizing $ heta$-generalized derivations on $L_0^{ obreak ext{infty}}(w)^*$ are actually $ heta$-right centralizers, clarifying their structure.

Findings

Every $ heta$-centralizing $ heta$-generalized derivation is a $ heta$-right centralizer.

The same result holds for $ heta$-skew centralizing $ heta$-generalized derivations.

Provides a characterization of these derivations in convolution algebras.

Abstract

Let $\theta$ be an isomorphism on $L_0^{\infty} (w)^*$. In this paper, we investigate $\theta$-generalized derivations on $L_0^{\infty} (w)^*$. We show that every $\theta$-centralizing $\theta$-generalized derivation on $L_0^{\infty} (w)^*$ is a $\theta$-right centralizer. We also prove that this result is true for $\theta$-skew centralizing $\theta$-generalized derivations.