Products of Toeplitz operators on the Bergman spaces $A_\alpha ^2$
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- by S. Pott and E. Strouse
- St. Petersburg Math. J. 18 (2007), 105-118
- DOI: https://doi.org/10.1090/S1061-0022-06-00945-9
- Published electronically: 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 $f,g$ analytic, to be bounded on the weighted Bergman space $L^2_a(\mathbb {D},(1-|z|^2)^\alpha dA)$. We also show that the only compact product of weighted Toeplitz operators is the trivial one.References
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Bibliographic 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
- 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
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 105-118
- MSC (2000): Primary 47B35, 32A36
- DOI: https://doi.org/10.1090/S1061-0022-06-00945-9
- MathSciNet review: 2225216