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The paper is devoted to a model and joint invariant subspaces under a pair of commuting isometries. A certain class of pairs of commuting isometries is defined. We give a… Click to show full abstract
The paper is devoted to a model and joint invariant subspaces under a pair of commuting isometries. A certain class of pairs of commuting isometries is defined. We give a model for such pairs and show that an arbitrary pair of commuting isometries has a minimal extension to a pair in the defined class. Subsequently we investigate a model for a general commuting pair of isometries via joint invariant subspaces of this extension. As an application operators of multiplication by independent variables on the Hardy space over the torus are extended to a pair in the defined class and joint invariant subspaces of the extension are described.
Journal Title: Integral Equations and Operator Theory
Year Published: 2019
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