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.

Keywords: Weakly compactly generated Banach space, locally compact\break group, $C^*$-algebra, Fourier- and Fourier-Stieltjes algebra, dual space

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