Ronald G. Douglas
Published 2010-09-22Version 1
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.
The invariant subspaces of $ S\oplus S^* $
Invariant subspaces of $\mathcal{H}^2(\mathbb{T}^2)$ and $L^2(\mathbb{T}^2)$ preserving compatibility
Invariant subspaces of the Cesaro operator
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