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

摘要

Let L_0~∞ 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)*.