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http://dx.doi.org/10.4134/CKMS.c170320

MODULE AMENABILITY AND MODULE ARENS REGULARITY OF WEIGHTED SEMIGROUP ALGEBRAS  

Asgari, Gholamreza (Department of Mathematics Central Tehran Branch Islamic Azad University)
Bodaghi, Abasalt (Department of Mathematics Garmsar Branch Islamic Azad University)
Bagha, Davood Ebrahimi (Department of Mathematics Central Tehran Branch Islamic Azad University)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 743-755 More about this Journal
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 amenble. 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;
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