Vol. 36, No. 2, 1971

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Invariant subspaces and projective representations

Keith Yale

Vol. 36 (1971), No. 2, 557–565
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
Authors
Keith Yale