St. Petersburg Mathematical Society

Author(s): S. Pott; 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
Posted: November 27, 2006
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Abstract: We give a sufficient and a necessary condition for the product of Toeplitz operators $T^\alpha_f T^\alpha_{\bar g}$ , with

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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Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 47B35, 32A36

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: 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): 3/OCT/2005
Posted: 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
Copyright of article: Copyright 2006, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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