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.
Oustad,K. (2021). On character amenability of weighted convolution algebras on certain semigroups. Mathematical Analysis and its Contemporary Applications, 3(2), 15-26. doi: 10.30495/maca.2021.1928647.1007
MLA
Oustad,K. . "On character amenability of weighted convolution algebras on certain semigroups", Mathematical Analysis and its Contemporary Applications, 3, 2, 2021, 15-26. doi: 10.30495/maca.2021.1928647.1007
HARVARD
Oustad K. (2021). 'On character amenability of weighted convolution algebras on certain semigroups', Mathematical Analysis and its Contemporary Applications, 3(2), pp. 15-26. doi: 10.30495/maca.2021.1928647.1007
CHICAGO
K. Oustad, "On character amenability of weighted convolution algebras on certain semigroups," Mathematical Analysis and its Contemporary Applications, 3 2 (2021): 15-26, doi: 10.30495/maca.2021.1928647.1007
VANCOUVER
Oustad K. On character amenability of weighted convolution algebras on certain semigroups. MACA, 2021; 3(2): 15-26. doi: 10.30495/maca.2021.1928647.1007
