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Module amenability and module Arens regularity of weighted semigroup algebras

Abasalt Bodaghi|Gholamreza Asgari|DAVOOD EBRAHIMI BAGHA
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회논문집 (Communications of the KMS)|제34권 제3호|pp. 743-755|DOI 10.4134/CKMS.c170320

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키워드

inverse semigroupmodule amenabilityBanach modulesmodule Arens regularity
주제분류수학

초록

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 $\omega$.

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 $\omega$.

참고문헌 (30)

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