Journal of Operator Theory
Volume 36, Issue 1, Summer 1996 pp. 63-71.
Projections of invariant subspaces and Toeplitz operatorsAuthors: 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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