Vol. 60, No. 2, 1975

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Algebraically irreducible representations of L1(G).

Robert A. Bekes

Vol. 60 (1975), No. 2, 11–25
Abstract

Let G be a locally compact, noncompact group and π a weakly continuous, uniformly bounded representation of G on a Hilbert space H. Suppose there exists a non-zero ξ in H such that the function x →⟨π(x)ξ,ξvanishes at infinity, Then π is not algebraically irreducible when lifted to a representation of L1(G). This implies that the left regular representation of L1(G), for G noncompact, contains no algebraically irreducible subrepresentations.

Mathematical Subject Classification 2000
Primary: 22D20
Milestones
Received: 24 April 1974
Published: 1 October 1975
Authors
Robert A. Bekes