A Unified Approach to the Arens Regularity and Related Problems for a Class of Banach Algebras Associated with Locally Compact Groups

Author:

Lau Anthony to-Ming1,Ülger Ali2

Affiliation:

1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada T6G 2G1

2. Department of Mathematics, Bogazici University, Bebek, Istanbul 34342, Turkey

Abstract

Abstract Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.

Funder

NSERC

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference24 articles.

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2. Convolution Operators on Groups

3. L’algèbre de Fourier d’un groupe localement compact;Eymard;Bulletin de la Société mathématique de France,1964

4. Arens regularity and the Ap(G) algebras;Forrest;Proc. Amer. Math. Soc.,1993

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