Weighted Semigroup Algebras as Dual Banach algebras

TL;DR

This paper investigates conditions under which weighted semigroup algebras become dual Banach algebras, providing theoretical insights and illustrative examples to deepen understanding of their duality properties.

Contribution

It establishes specific criteria for weighted semigroup algebras to be dual Banach algebras and offers illustrative examples to demonstrate these conditions.

Findings

Identifies conditions for $ ext{ell}^1(S, ext{omega})$ to be a dual Banach algebra

Provides examples illustrating the duality properties of weighted semigroup algebras

Enhances understanding of the structure of dual Banach algebras in the context of weighted semigroups

Abstract

In this paper, among other things, we study those conditions under which the weighted semigroup algebra $\ell^1(S,\omega)$ is a dual Banach algebra with respect to predual $c_0(S)$. Some useful examples, illustrating the results, are also included.