On the maximal and minimal Left ideals of certain Banach algebras on locally compact groups

Abstract

Let L∞0(G) be the Banach space of all essentially bounded measurable functions on a locally compact group G vanishing at infinity. In this paper, we describe maximal and minimal left ideals in the Banach algebra L∞0(G)∗ equipped with an Arens type product. We also investigate some spectral properties of L∞0(G)∗ .

Keywords: Arens product, locally compact group, maximal ideal, radical.