Homological propeties of Bimeasure algebras and their BSE properties

Let \(G\) and \(H\) be locally compact groups. \(BM(G, H)\) denoted the Banach algebra of bounded bilinear forms on \(C_{0}(G)\times C_{0}(H)\).In this paper, the homological properties of Bimeasure algebras are investigated. It is found and approved that the Bimeasure algebras \(BM(G, H)\) is amena...

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Bibliographic Details
Published in:arXiv.org 2023-01
Main Authors: Aghakoochai, Maryam, Rejali, Ali
Format: Article
Language:English
Subjects:
Algebra
Banach spaces
Homology
Online Access:Get full text
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Summary:Let \(G\) and \(H\) be locally compact groups. \(BM(G, H)\) denoted the Banach algebra of bounded bilinear forms on \(C_{0}(G)\times C_{0}(H)\).In this paper, the homological properties of Bimeasure algebras are investigated. It is found and approved that the Bimeasure algebras \(BM(G, H)\) is amenable if and only if \(G\) and \(H\) are discrete. The correlation between the weak amenability of \(BM(G, H)\) and \(M(G\times H)\) is assessed. It is found and approved that the biprojectivity of the bimeasure algebra \(BM(G, H)\) is equivalent to the finiteness of \(G\) and \(H\). Furthermore, we show that the bimeasure group algebra \(BM_{a}(G, H)\) is a BSE algebra. It will be concluded that \(BM(G, H)\) is a BSE- algebra if and only if \(G\) and \(H\) are discrete groups.
ISSN:2331-8422