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Powers and roots of Toeplitz operators


Author: Issam Louhichi
Journal: Proc. Amer. Math. Soc. 135 (2007), 1465-1475
MSC (2000): Primary 47B35; Secondary 47L80
DOI: https://doi.org/10.1090/S0002-9939-06-08626-6
Published electronically: November 29, 2006
MathSciNet review: 2276656
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the commutativity of two Toeplitz operators whose symbols are quasihomogeneous functions. We give a relationship between this commutativity and the roots (or powers) of the Toeplitz operators. We use this to characterize Toeplitz operators with symbols in $ L^{\infty}(\mathbb{D})$ which commute with Toeplitz operators whose symbols are of the form $ e^{ip\theta}r^m$.


References [Enhancements On Off] (What's this?)

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Additional Information

Issam Louhichi
Affiliation: UFR Mathématiques et Informatique, Université Bordeaux 1, 351 cours de la Libération, 33405 Talence, France
Email: louhichi@math.u-bordeaux1.fr

DOI: https://doi.org/10.1090/S0002-9939-06-08626-6
Keywords: Toeplitz operators, Bergman space, Mellin transform.
Received by editor(s): March 26, 2005
Received by editor(s) in revised form: December 20, 2005
Published electronically: November 29, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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