Compact elements of weighted group algebras

Fereidoun Ghahramani

Vol. 113 (1984), No. 1, 77–84

DOI: 10.2140/pjm.1984.113.77

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 T_g(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