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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Powers and roots of Toeplitz operators


Author: Issam Louhichi
Journal: Proc. Amer. Math. Soc. 135 (2007), 1465-1475
MSC (2000): Primary 47B35; Secondary 47L80
Published electronically: November 29, 2006
MathSciNet review: 2276656
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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$.


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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: http://dx.doi.org/10.1090/S0002-9939-06-08626-6
PII: S 0002-9939(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.