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Weak amenability for dual Banach algebras

Part of: Topological algebras, normed rings and algebras, Banach algebras Abstract harmonic analysis Locally compact groups and their algebras

Published online by Cambridge University Press:  29 April 2024

Amin Mahmoodi Open the ORCID record for Amin Mahmoodi [Opens in a new window]
Amin Mahmoodi*
Affiliation:
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
*
Email: a_mahmoodi@iauctb.ac.ir
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Abstract

A suitable notion of weak amenability for dual Banach algebras, which we call weak Connes amenability, is defined and studied. Among other things, it is proved that the measure algebra M(G) of a locally compact group G is always weakly Connes amenable. It can be a complement to Johnson’s theorem that $L^1(G)$ is always weakly amenable [10].

Keywords

dual Banach algebraConnes amenabilityweak amenabilityweak Connes amenability

MSC classification

Primary: 22D15: Group algebras of locally compact groups 43A10: Measure algebras on groups, semigroups, etc.
Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc. 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 9
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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