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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Products of Toeplitz operators on the Bergman spaces $ A_\alpha^2$


Authors: S. Pott and E. Strouse
Original publication: Algebra i Analiz, tom 18 (2006), nomer 1.
Journal: St. Petersburg Math. J. 18 (2007), 105-118
MSC (2000): Primary 47B35, 32A36
Published electronically: November 27, 2006
MathSciNet review: 2225216
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a sufficient and a necessary condition for the product of Toeplitz operators $ T^\alpha_f T^\alpha_{\bar g}$, with $ f,g$ analytic, to be bounded on the weighted Bergman space $ L^2_a(\mathbb{D},(1-\vert z\vert^2)^\alpha dA)$. We also show that the only compact product of weighted Toeplitz operators is the trivial one.


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Additional Information

S. Pott
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom
Email: sp@maths.gla.ac.uk

E. Strouse
Affiliation: Departement de Mathématiques Pures, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, France
Email: Elizabeth.Strouse@math.u-bordeaux1.fr

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00945-9
PII: S 1061-0022(06)00945-9
Keywords: Weighted Bergman spaces, Toeplitz operators, reproducing kernel thesis
Received by editor(s): October 3, 2005
Published electronically: November 27, 2006
Additional Notes: This work was supported by the European Network on Analysis and Operators (HPRN CT 2000 00116), by a grant by the Nuffield Foundation, and by EPSRC. The first author would like to thank the Departement de Mathématiques Pures, Université Bordeaux I, for their hospitality
Article copyright: © Copyright 2006 American Mathematical Society