%0 Journal Article %T On character amenability of weighted convolution algebras on certain semigroups %J Mathematical Analysis and its Contemporary Applications %I Research & Science Group Ltd %Z 2716-9898 %A Oustad, Kobra %D 2021 %\ 06/01/2021 %V 3 %N 2 %P 15-26 %! On character amenability of weighted convolution algebras on certain semigroups %K Character amenability %K Rees matrix semigroup %K Weighted Rees matrix semigroup algebra %K Clifford semigroup %R 10.30495/maca.2021.1928647.1007 %X 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. %U https://www.macajournal.com/article_682819_94981018730a45952305489b3d587939.pdf