On the Maximal and Minimal Left Ideals of Certain Banach Algebras on Locally Compact Groups
Department of Mathematics, Zanjan University, 313, Zanjan, Iran
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.