Algebraically irreducible representations of L₁(G).

Robert A. Bekes

Vol. 60 (1975), No. 2, 11–25

DOI: 10.2140/pjm.1975.60.11

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,ξ⟩ vanishes 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