On approximate Connes-biprojectivity of dual Banach algebras
S. F. Shariati, A. Pourabbas, A. Sahami

TL;DR
This paper introduces the concept of approximate Connes-biprojectivity for dual Banach algebras, explores its relations with other properties, and characterizes when certain algebras are approximately Connes-biprojective.
Contribution
It defines approximate Connes-biprojectivity, establishes criteria for dual triangular Banach algebras, and characterizes this property for group measure algebras and $L^2$ spaces.
Findings
$M(G)$ is approximately Connes-biprojective iff $G$ is amenable
Certain dual triangular Banach algebras are not approximately Connes-biprojective
For an infinite compact group $G$, $L^2(G)$ is approximately Connes-biprojective but not Connes-biprojective.
Abstract
In this paper, we introduce a notion of approximate Connes-biprojectivity for dual Banach algebras. We study the relation between approximate Connes-biprojectivity, Johnson pseudo-Connes amenability and -Connes amenability. We propose a criterion to show that some certain dual triangular Banach algebras are not approximately Connes-biprojective. Next we show that for a locally compact group , the Banach algebra is approximately Connes-biprojective if and only if is amenable. Finally for an infinite commutative compact group we show that the Banach algebra with convolution product is approximately Connes-biprojective, but it is not Connes-biprojective.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Topics in Algebra
