Toeplitz operators on the polydisk
HTML articles powered by AMS MathViewer
- by Sunhua Sun and Dechao Zheng PDF
- Proc. Amer. Math. Soc. 124 (1996), 3351-3356 Request permission
Abstract:
In this paper it is shown that two analytic Toeplitz operators essentially doubly commute if and only if they doubly commute on the Bergman space of the polydisk.References
- Patrick Ahern, Manuel Flores, and Walter Rudin, An invariant volume-mean-value property, J. Funct. Anal. 111 (1993), no. 2, 380–397. MR 1203459, DOI 10.1006/jfan.1993.1018
- Sheldon Axler and Pamela Gorkin, Algebras on the disk and doubly commuting multiplication operators, Trans. Amer. Math. Soc. 309 (1988), no. 2, 711–723. MR 961609, DOI 10.1090/S0002-9947-1988-0961609-9
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
- De Chao Zheng, Hankel operators and Toeplitz operators on the Bergman space, J. Funct. Anal. 83 (1989), no. 1, 98–120. MR 993443, DOI 10.1016/0022-1236(89)90032-3
Additional Information
- Sunhua Sun
- Affiliation: Department of Mathematics, Sichuan University, Chengdu, People’s Republic of China
- Dechao Zheng
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Address at time of publication: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- MR Author ID: 229147
- Received by editor(s): October 6, 1994
- Received by editor(s) in revised form: April 21, 1995
- Additional Notes: The first author was supported in part by the National Natural Science Foundation of China
The second author was supported in part by the National Science Foundation - Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3351-3356
- MSC (1991): Primary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-96-03425-9
- MathSciNet review: 1328380