$θ$-derivations on convolution algebras

M. Eisaei, Gh. R. Moghimi

Published 2024-03-27Version 1

In this paper, we investigate $\theta$-derivations on Banach algebra $ L_0^{\infty} (w)^*$. First, we study the range of them and prove the Singer-Wermer conjucture. We also give a characterization of the space of all $\theta$-derivations on $ L_0^{\infty} (w)^*$. Then, we prove automatic continuity and Posner's theorems for $\theta$-derivations.