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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unitary equivalence to a truncated Toeplitz operator: analytic symbols
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by Stephan Ramon Garcia, Daniel E. Poore and William T. Ross PDF
Proc. Amer. Math. Soc. 140 (2012), 1281-1295 Request permission

Abstract:

Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this paper we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive, and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension $\leq 3$ is unitarily equivalent to a direct sum of truncated Toeplitz operators.
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Additional Information
  • Stephan Ramon Garcia
  • Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
  • MR Author ID: 726101
  • Email: Stephan.Garcia@pomona.edu
  • Daniel E. Poore
  • Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
  • Email: dep02007@mymail.pomona.edu
  • William T. Ross
  • Affiliation: Department of Mathematics and Computer Science, University of Richmond, Richmond, Virginia 23173
  • MR Author ID: 318145
  • Email: wross@richmond.edu
  • Received by editor(s): December 21, 2010
  • Published electronically: July 22, 2011
  • Additional Notes: The first author was partially supported by National Science Foundation Grant DMS-1001614.
  • Communicated by: Richard Rochberg
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1281-1295
  • MSC (2010): Primary 47A05, 47B35, 47B99
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11060-8
  • MathSciNet review: 2869112