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Compactness of a Locally Compact Group G and Geometric Properties of Ap(G)

Published online by Cambridge University Press:  20 November 2018

Tianxuan Miao
Tianxuan Miao*
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7E 5E1 e-mail: tmiao@thunder.lakeheadu.ca
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Abstract

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Let G be a locally compact topological group. A number of characterizations are given of the class of compact groups in terms of the geometric properties such as Radon-Nikodym property, Dunford-Pettis property and Schur property of Ap(G), and the properties of the multiplication operator on PFp(G). We extend and improve several results of Lau and Ülger [17] to Ap(G) and Bp(G) for arbitrary p.

Keywords

43A07Locally compact groupsamenable groupsHerz algebraRadon-Nikodym propertyDunford-Pettis propertySchur property
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 6 , 01 December 1996 , pp. 1273 - 1285
Copyright
Copyright © Canadian Mathematical Society 1996

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