Proceedings of the American Mathematical Society

Author(s): Sheldon Axler; Zeljko Cuckovic; N. V. Rao
Journal: Proc. Amer. Math. Soc. 128 (2000), 1951-1953.
MSC (2000): Primary 47B35
Posted: October 29, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract: In this note we show that if two Toeplitz operators on a Bergman space commute and the symbol of one of them is analytic and nonconstant, then the other one is also analytic.

1.: Sheldon Axler and \v{Z}eljko \v{C}u\v{c}kovi\'{c}, Commuting Toeplitz Operators with harmonic symbols, Integral Equations Operator Theory 14 (1991), 1-12. MR 92f:4018
2.: Sheldon Axler and Allen Shields, Algebras generated by analytic and harmonic functions, Indiana Univ. Math. J. 36 (1987), 631-638. MR 88h:46102
3.: Christopher J. Bishop, Approximating continuous functions by holomorphic and harmonic functions, Trans. Amer. Math. Soc. 311 (1989), 781-811. MR 89j:30051
4.: Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1964), 89-102. MR 28:3350
5.: E. M. \v{C}irka, Approximation by holomorphic functions on smooth manifolds in $\mathbf C^n$ , Mat. Sb. 78 (1969), 101-123. MR 39:480
6.: Carl C. Cowen, The commutant of an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978), 1-31. MR 58:2420
7.: \v{Z}eljko \v{C}u\v{c}kovi\'{c}, Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), 277-285. MR 94j:47041
8.: \v{Z}eljko \v{C}u\v{c}kovi\'{c} and N. V. Rao, Mellin Transform, monomial symbols and commuting Toeplitz operators, J. Funct. Anal. 154 (1998), 195-214. MR 99f:47033
9.: Alexander J. Izzo, Uniform algebras generated by holomorphic and pluriharmonic functions, Trans. Amer. Math. Soc. 339 (1993), 835-847. MR 93m:46060
10.: James E. Thomson, The commutant of a class of analytic Toeplitz operators, Amer. J. Math. 99 (1977), 522-529. MR 57:1181
11.: James Thomson, The commutant of a class of analytic Toeplitz operators II, Indiana Univ. Math. J. 25 (1976), 793-800. MR 54:5891

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B35

Sheldon Axler
Affiliation: Department of Mathematics, San Francisco State University, San Francisco, California 94132
Email: axler@sfsu.edu

Zeljko Cuckovic
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606
Email: zcuckovi@math.utoledo.edu

N. V. Rao
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606
Email: rnagise@math.utoledo.edu

DOI: 10.1090/S0002-9939-99-05436-2
PII: S 0002-9939(99)05436-2
Received by editor(s): August 8, 1998
Posted: October 29, 1999
Additional Notes: The first author was partially supported by the National Science Foundation
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS