Connes-biprojective dual Banach algebra
Ahmad Shirinkalam, A. Pourabbas

TL;DR
This paper introduces the concept of Connes-biprojectivity for dual Banach algebras, explores its relation to Connes-amenability, and establishes conditions under which dual and Arens regular Banach algebras exhibit this property.
Contribution
It defines Connes-biprojectivity for dual Banach algebras and links it to Connes-amenability, providing new insights into the structure of these algebras.
Findings
Connes-amenability is equivalent to Connes-biprojectivity plus having a bounded approximate identity.
For Arens regular biprojective Banach algebras, their second duals are Connes-biprojective.
Introduces a new notion of biprojectivity tailored for dual Banach algebras.
Abstract
In this paper, we introduce a new notion of biprojectivity, called Connes-biprojective, for dual Banach algebras. We study the relation between this new notion to Connes-amenability and we show that, for a given dual Banach algebra , it is Connes-amenable if and only if is Connes-biprojective and has a bounded approximate identity. Also, for an Arens regular Banach algebra , we show that if is biprojective, then the dual Banach algebra is Connes-biprojective.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
