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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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On a class of jointly hyponormal Toeplitz operators
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by Caixing Gu PDF
Trans. Amer. Math. Soc. 354 (2002), 3275-3298 Request permission

Abstract:

We characterize when a pair of Toeplitz operators $\mathbf {T}=(T_{\phi },T_{\psi })$ is jointly hyponormal under various assumptions—for example, $\phi$ is analytic or $\phi$ is a trigonometric polynomial or $\phi -\psi$ is analytic. A typical characterization states that $\mathbf {T}=(T_{\phi },T_{\psi })$ is jointly hyponormal if and only if an algebraic relation of $\phi$ and $\psi$ holds and the single Toeplitz operator $T_{\omega }$ is hyponormal, where $\omega$ is a combination of $\phi$ and $\psi$. More general results for an $n$-tuple of Toeplitz operators are also obtained.
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Additional Information
  • Caixing Gu
  • Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
  • MR Author ID: 236909
  • ORCID: 0000-0001-6289-7755
  • Email: cgu@calpoly.edu
  • Received by editor(s): December 28, 1999
  • Received by editor(s) in revised form: February 9, 2001, and December 3, 2001
  • Published electronically: April 3, 2002
  • Additional Notes: Partially supported by the National Science Foundation Grant DMS-9706838.
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 3275-3298
  • MSC (2000): Primary 47B35, 47B20
  • DOI: https://doi.org/10.1090/S0002-9947-02-03001-5
  • MathSciNet review: 1897400