New York Journal of Mathematics
Volume 17a (2011) 1-10


Ronald G. Douglas

Variations on a theme of Beurling

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Published: January 30, 2011
Keywords: Invariant subspaces, Beurling's Theorem, Hilbert modules
Subject: 46E22, 46J10, 47A15.

Interpretations of the Beurling-Lax-Halmos Theorem on invariant subspaces of the unilateral shift are explored using the language of Hilbert modules. Extensions and consequences are considered in both the one and multivariate cases with an emphasis on the classical Hardy, Bergman and Drury-Arveson spaces.


During the time the research leading up to this note was carried out, the author was partially supported by a grant from the National Science Foundation.

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Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368\quad