Complex symmetric operators and applications
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- by Stephan Ramon Garcia and Mihai Putinar PDF
- Trans. Amer. Math. Soc. 358 (2006), 1285-1315 Request permission
Abstract:
We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.References
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Additional Information
- Stephan Ramon Garcia
- Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080
- MR Author ID: 726101
- Email: garcias@math.ucsb.edu
- Mihai Putinar
- Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080
- MR Author ID: 142835
- Email: mputinar@math.ucsb.edu
- Received by editor(s): February 21, 2004
- Received by editor(s) in revised form: May 10, 2004
- Published electronically: May 26, 2005
- Additional Notes: The second author was supported in part by NSF Grant DMS #0100367.
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 1285-1315
- MSC (2000): Primary 30D55, 47A15
- DOI: https://doi.org/10.1090/S0002-9947-05-03742-6
- MathSciNet review: 2187654