On pseudo-amenability of Beurling algebras

Abstract

Amenability and pseudo-amenability of $ \ell^{1}(S,\omega) $ ischaracterized, where $S$ is a left (right) zero semigroup or it is arectangular band semigroup. The equivalence conditions toamenability of $\ell^{1}(S,\omega)$ are provided, where  $ S $ is aband semigroup. The equivalence properties of amenability of$\ell^{1}(S, \omega)^{**}$ are described, where $S$ is an inversesemigroup. For a locally compact group $G$, pseudo-amenability of $\ell^{1}(G,\omega) $ is also discussed.