Journal of Operator Theory

Volume 40, Issue 2, Fall 1998 pp. 323-337.

Weakly compactly generated Banach algebras associated to locally compact groups

Authors: E. Kaniuth (1), A.T. Lau (2), and G. Schlichting (3)
Author institution: (1) Fachbereich Mathematik/Informatik, Universitaet Paderborn, D-33095, Paderborn, Germany
(2) Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
(3) Mathematisches Institut, Technische Universitaet Muenchen, D-80290 Muenchen, Germany

Summary: Let

$G$ be a locally compact group, and let

$X$ be any one of the Banach algebras

$C^*(G)$ ,

$C_0(G)$ ,

$B(G)$ or

$A(G)$ . We characterize the property that

$X$ , as a Banach space, is weakly compactly generated in terms of conditions on

$G$ and its dual space.

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