Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Partially isometric dilations of noncommuting -tuples of operators

Author(s): Michael T. Jury; David W. Kribs
Journal: Proc. Amer. Math. Soc. 133 (2005), 213-222.
MSC (2000): Primary 47A20, 47A45
Posted: June 23, 2004
MathSciNet review: 2085172
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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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