On character amenability of weighted convolution algebras on certain semigroups

In this work, we study the character amenability of weighted convolution algebras \ell^{۱} (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^{۱} (S,\omega) is character amenable if each maximal semigroup of S is amenable. Then for a commutative semigroup S and \omega(x)\geq ۱, for all x\in S . Moreover, we show that character amenability of \ell^{۱} (S,\omega) implies that S is a Clifford semigroup. Finally, we investigate the character amenability of the weighted convolution algebra \ell^{۱} (S,\omega), and its second dual for a Rees matrix semigroup.

Keywords:

Character amenability , Rees matrix semigroup , Weighted Rees matrix semigroup algebra , Clifford semigroup