Weighted group algebras
Maryam Aghakoochai, Ali Rejali

TL;DR
This paper investigates the algebraic and topological properties of weighted group algebras on locally compact Abelian groups, establishing conditions for regularity and Tauberian properties based on the weight function.
Contribution
It characterizes when weighted group algebras are regular and Tauberian, linking these properties to the nature of the weight function.
Findings
Weighted group algebra $L^{1}(G, w)$ is regular iff $w$ is nonquasianalytic.
$L^{1}(G, w)$ is Tauberian for any Borel measurable weight.
Provides criteria connecting weight functions to algebraic properties.
Abstract
Let be a locally compact Abelian group, and be a Borel measurable weighted function. In this paper, the algebraic and topological properties of group algebra are studied and assessed. We show that the weighted group algebra is regular if and only if is a nonquasianalytic weight function. Also is Tauberian, for any Borel measurable weight function on the group .
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
