Document Type : Original Article

Author

Department of Mathematics, Dehdasht Branch, Islamic Azad University, Dehdasht, Iran

Abstract

In this work, we study the character amenability of weighted convolution algebras $\ell^{1} (S,\omega)$, where $S$ is a semigroup of classes of inverse semigroups with a uniformly locally finite idempotent set, inverse semigroups with a finite number of idempotents, Clifford semigroups and Rees matrix semigroups. We show that for inverse semigroup with a finite number of idempotents and any weight $\omega$, $\ell^{1} (S,\omega)$ is character amenable if each maximal semigroup of $S$ is amenable. Then for a commutative semigroup $S$ and $\omega(x)\geq 1$, for all $x\in S$. Moreover, we show that character amenability of $\ell^{1} (S,\omega)$ implies that $S$ is a Clifford semigroup. Finally, we investigate the character amenability of the weighted convolution algebra $\ell^{1} (S,\omega)$, and its second dual for a Rees matrix semigroup.

Keywords