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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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.
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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