Module amenability and module Arens regularity of weighted semigroup algebras
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 743-755
Published online July 31, 2019
Gholamreza Asgari, Abasalt Bodaghi, Davood Ebrahimi Bagha
Islamic Azad University; Islamic Azad University; Islamic Azad University
Abstract : For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, necessary and sufficient conditions are obtained for the weighted semigroup algebra $l ^{1}(S,\omega)$ and its second dual to be $l ^{1}(E)$-module amen\-ble. Some results for the module Arens regularity of $l ^{1}(S,\omega)$ (as an $l ^{1}(E)$-module) are found. If $S$ is either of the bicyclic inverse semigroup or the Brandt inverse semigroup, it is shown that $l ^{1}(S, \omega)$ is module amenable but not amenable for any weight $\omega$.
Keywords : Banach modules, inverse semigroup, module Arens regularity, module amenability
MSC numbers : 43A10, 43A20, 46H20, 20M18
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