Partially Isometric Dilations of Noncommuting $N$-tuples of Operators

David W. Kribs; Michael T. Jury

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Partially Isometric Dilations of Noncommuting N-tuples of Operators

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arxiv math/0309398 v1 pith:THA66A5U submitted 2003-09-24 math.FA math.OA

Partially Isometric Dilations of Noncommuting N-tuples of Operators

Michael T. Jury , David W. Kribs This is my paper

classification math.FA math.OA

keywords contractiondilationsoperatorsdilationisometriespartialpartiallyspace

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Given a row contraction of operators on Hilbert space and a family of projections on the space which stabilize the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries which satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold Decomposition for partial isometries to describe the models for these dilations, and discuss how the basic properties of a dilation depend on the row contraction.

Partially Isometric Dilations of Noncommuting N-tuples of Operators

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