Vol. 113, No. 1, 1984

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ISSN: 0030-8730
Compact elements of weighted group algebras

Fereidoun Ghahramani

Vol. 113 (1984), No. 1, 77–84
Abstract

For a locally compact group G let L1(G,ωλ) be the weighted group algebra. We characterize elements g L1(G,ωλ) for which the operator Tg(f) = f g(f L1(G,ωλ)) is compact We conclude a result due to S. Sakai that if G is a locally compact non-compact group, then 0 is the only compact element of L1(G,λ), and a result due to C. Akemann that if G is a compact group, then every element of L1(G,λ) is compact.

Mathematical Subject Classification 2000
Primary: 43A20
Secondary: 43A22, 47B05
Milestones
Received: 3 May 1982
Revised: 22 February 1983
Published: 1 July 1984
Authors
Fereidoun Ghahramani