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.References
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Additional Information
- Michael T. Jury
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 742791
- Email: jury@math.purdue.edu
- David W. Kribs
- Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- Email: dkribs@uoguelph.ca
- Received by editor(s): June 13, 2003
- Received by editor(s) in revised form: September 29, 2003
- Published electronically: June 23, 2004
- Communicated by: Joseph A. Ball
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 213-222
- MSC (2000): Primary 47A20, 47A45
- DOI: https://doi.org/10.1090/S0002-9939-04-07547-1
- MathSciNet review: 2085172