Partially isometric dilations of noncommuting 𝑁-tuples of operators

Jury, Michael; Kribs, David

doi:10.1090/S0002-9939-04-07547-1

Partially isometric dilations of noncommuting $N$-tuples of operators
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by Michael T. Jury and David W. Kribs PDF

Proc. Amer. Math. Soc. 133 (2005), 213-222 Request permission

Abstract:

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that 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 we discuss how the basic properties of a dilation depend on the row contraction.

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