Cohomological properties and Arens regularity of Banach algebras
Hossein Eghbali Sarai, Kazem Haghnejad Azar, Ali Jabbari

TL;DR
This paper investigates cohomological properties of Banach algebras, exploring conditions for Arens regularity and reflexivity, and analyzing the vanishing of Hochschild cohomology groups in various contexts.
Contribution
It provides new insights into the cohomological structure of Banach algebras, linking amenability, Arens regularity, and reflexivity with specific algebraic and topological conditions.
Findings
Vanishing of certain Hochschild cohomology groups for Banach algebras.
Conditions under which the second transpose of a derivation implies Arens regularity.
Characterization of reflexivity in dual left strongly irregular Banach algebras with amenable second dual.
Abstract
In this paper, we study some cohomlogical properties of Banach algebras. For a Banach algebra and a Banach -bimodule , we investigate the vanishing of the first Hochschild cohomology groups and , where . For amenable Banach algebra , we show that there are Banach -bimodules , and elements such that where, for every , and for every . Moreover, under a condition, we show that if the second transpose of a continuous derivation from the Banach algebra into i.e., a continuous linear map from into , is a derivation, then is Arens regular. Finally, we show that if is a dual…
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
