The structure of \(\varphi\)-module amenable Banach algebras
type: Item
instance of: scholarly article
title: The structure of \(\varphi\)-module amenable Banach algebras
zbMATH Open document ID: 1470.46075
DOI: 10.1155/2014/176736
author: Mahmood Lashkarizadeh Bami
author: M. Valaei
author: Massoud Amini
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study the concept of \(\varphi\)-module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. Also, we compare the notions of \(\varphi\)-amenability and \(\varphi\)-module amenability of Banach algebras. As a consequence, we show that, if \(S\) is an inverse semigroup with finite set \(E\) of idempotents and \(l^1 \left(S\right)\) is a commutative Banach \(l^1 \left(E\right)\)-module, then \(l^1 \left(S\right)^{* *}\) is \(\varphi^{* *}\)-module amenable if and only if \(S\) is finite, when \(\varphi \in \mathrm{Hm}_{l^1 \left(E\right)} \left(l^1 \left(S\right)\right)\) is an epimorphism. Indeed, we have generalized a well-known result due to \textit{F. Ghahramani} et al. [Proc. Am. Math. Soc. 124, No. 5, 1489--1497 (1996; Zbl 0851.46035)].
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 43A07
zbMATH DE Number: 7021874
Wikidata QID: Q59035783
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/176736
OpenAlex ID: W2007384763
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description: scientific article; zbMATH DE number 7021874