Invariant subspaces and projective representations

Keith Yale

Vol. 36 (1971), No. 2, 557–565

DOI: 10.2140/pjm.1971.36.557

Abstract

Let Γ be a subgroup of the real line R with the discrete topology, and let G be its compact dual group. This paper shows the existence of a (nontrivial) simply invariant subspace of L²(G) which is not of the form φH²(G) provided Γ contains at least two rationally independent elements. The proof relies heavily on the existence of a nontrivial locaI projective representation of the two-dimensional torus.

Mathematical Subject Classification

Primary: 42.50

Secondary: 46.00

Milestones

Received: 22 April 1969

Published: 1 February 1971