10.30495/maca.2021.1928647.1007

On character amenability of weighted convolution algebras on certain semigroups

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  • Kobra Oustad1,
  1. Department of Mathematics, Dehdasht Branch, Islamic Azad University, Dehdasht, Iran

Published in Issue 2021-04-01

How to Cite

On character amenability of weighted convolution algebras on certain semigroups. (2021). Mathematical Analysis and Its Contemporary Applications, 3(2). https://doi.org/10.30495/maca.2021.1928647.1007

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Abstract

In this work, we study the character amenability of weighted convolution algebras ℓ1(S, ω), 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 ω, ℓ1(S, ω) is character amenable if each maximal semigroup of S is amenable. Then for a commutative semigroup S and ω(x) ≥1, for all x ∈S. Moreover, we show that character amenability of ℓ1(S, ω) implies that S is a Clifford semigroup. Finally, we investigate the character amenability of the weighted convolution algebra ℓ1(S, ω), and its second dual for a Rees matrix semigroup.

Keywords

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