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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On a class of jointly hyponormal Toeplitz operators


Author: Caixing Gu
Journal: Trans. Amer. Math. Soc. 354 (2002), 3275-3298
MSC (2000): Primary 47B35, 47B20
Published electronically: April 3, 2002
MathSciNet review: 1897400
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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
Email: cgu@calpoly.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03001-5
PII: S 0002-9947(02)03001-5
Keywords: Toeplitz operator, Hankel operator, joint hyponormality
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.
Article copyright: © Copyright 2002 American Mathematical Society