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Toeplitz operators on the polydisk

Authors: Sunhua Sun and Dechao Zheng
Journal: Proc. Amer. Math. Soc. 124 (1996), 3351-3356
MSC (1991): Primary 47B35
MathSciNet review: 1328380
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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 [Enhancements On Off] (What's this?)

  • [AFR] P. Ahern, M. Flores and W. Rudin, An invariant volume-mean-value property, J. Funct. Anal. 111 (1993), 380--397. MR 94b:31002
  • [AG] S. Axler and P. Gorkin, Algebras on the disk and doubly commuting operators, Trans. Amer. Math. Soc. 309 (1988), 711--723. MR 90a:46133
  • [R] W. Rudin, Function theory on the polydiscs, Benjamin, New York, 1969. MR 41:501
  • [SW] E. M. Stein and G. Weiss, Introduction to Fourier analysis on euclidean spaces, Princeton Univ. Press, 1971. MR 46:4102
  • [Z] D. Zheng, Hankel operators and Toeplitz operators on the Bergman space, J. Funct. Anal. 83 (1989), 98--120. MR 91b:47057

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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

Keywords: Toeplitz operator, Bergman space, polydisk
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
Article copyright: © Copyright 1996 American Mathematical Society

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