On $\hat{I}¸$-centralizing $\hat{I}¸$-generalized derivations on convolution algebras

Abstract

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