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

On the Maximal and Minimal Left Ideals of Certain Banach Algebras on Locally Compact Groups

Saeid Maghsoudi

Department of Mathematics, Zanjan University, 313, Zanjan, Iran

Rasoul Nasr-Isfahani

Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

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.

MSC: Primary 43A15, 43A20, Secondary 46H05.