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Commutants of Toeplitz operators on the ball and annulus

Published online by Cambridge University Press:  18 May 2009

Željko Čučković  and
Dashan Fan
Željko Čučković
Affiliation:
Department of Mathematics, University of Wisconsin Centers, Waukesha, WI 53188, U.S.A.
Dashan Fan
Affiliation:
Department of Mathematical Sciences, University Of Wisconsin-Milwaukee, Milwaukee, WI 53201, U.S.A.
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In this paper we study commutants of Toeplitz operators with polynomial symbols acting on Bergman spaces of various domains. For a positive integer n, let V denote the Lebesgue volume measure on ℂn. If ω is a domain in ℂn, then the Bergman space is defined to be the set of all analytic functions from ω into ℂ such that

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 303 - 309
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Baker, I. N., Deddens, J. A. and Ullman, J. L., A theorem on entire functions with applications to Toeplitz operators, Duke Math. J. 41 (1974), 739–745.CrossRefGoogle Scholar
2.Cowen, C. C., The commutant dof an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978) 1–31.CrossRefGoogle Scholar
3.Čučković, Č., Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), 277–285.CrossRefGoogle Scholar
4.Deddens, J. A. and Wong, T. K., The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc. 184 (1973), 261–273.CrossRefGoogle Scholar
5.Shields, A. L. and Wallen, L. J., The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1970–1971), 777–788.CrossRefGoogle Scholar
6.Thomson, J. E., The commutants of a class of analytic Toeplitz operators, Amer. J. Math. 99 (1977), 522–529.CrossRefGoogle Scholar
7.Wallsten, R., Hankel operators between weighted Bergman spaces on the ball, Ark. Mat. 28 (1990), 183–192.CrossRefGoogle Scholar