Journal of Operator Theory

Volume 36, Issue 1, Summer 1996 pp. 63-71.

Projections of invariant subspaces and Toeplitz operators

Authors: Kai Hing Lum
Author institution:Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, S(0511), REPUBLIC OF SINGAPORE

Summary: Let K be a compact abelian group dual to a discrete abelian group which possesses an archimedean linear order. Let W = EH^2(K) be a Beurling subspace of L^2(K), where H^2(K) is the space of analytic functions and E is a unimodular function on K. We show that if E satisfies an approximation condition, then there is a standard invariant subspace H so that the orthogonal projection $pr : W \to H$ is injective and has dense range. We explain that this kind of consideration can be regarded as a generalization of the study of Toeplitz operators.

Keywords: Orthogonal projections, Beurling subspaces, compact abelian groups.

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