Commutants of analytic Toeplitz operators on the Bergman space
Authors:
Sheldon Axler, Željko Čučković and N. V. Rao
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1951-1953
MSC (2000):
Primary 47B35
DOI:
https://doi.org/10.1090/S0002-9939-99-05436-2
Published electronically:
October 29, 1999
MathSciNet review:
1694299
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- Sheldon Axler and Željko Čučković, Commuting Toeplitz Operators with harmonic symbols, Integral Equations Operator Theory 14 (1991), 1–12.
- Sheldon Axler and Allen Shields, Algebras generated by analytic and harmonic functions, Indiana Univ. Math. J. 36 (1987), no. 3, 631–638. MR 905614, DOI https://doi.org/10.1512/iumj.1987.36.36034
- Christopher J. Bishop, Approximating continuous functions by holomorphic and harmonic functions, Trans. Amer. Math. Soc. 311 (1989), no. 2, 781–811. MR 961619, DOI https://doi.org/10.1090/S0002-9947-1989-0961619-2
- Arlen Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89–102. MR 160136, DOI https://doi.org/10.1007/978-1-4613-8208-9_19
- E. M. Čirka, Approximation by holomorphic functions on smooth manifolds in ${\bf C}^{n}$, Mat. Sb. (N.S.) 78 (120) (1969), 101–123 (Russian). MR 0239121
- Carl C. Cowen, The commutant of an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978), 1–31. MR 482347, DOI https://doi.org/10.1090/S0002-9947-1978-0482347-9
- Željko Čučković, Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), no. 2, 277–285. MR 1251902
- Željko C̆učković and N. V. Rao, Mellin transform, monomial symbols, and commuting Toeplitz operators, J. Funct. Anal. 154 (1998), no. 1, 195–214. MR 1616532, DOI https://doi.org/10.1006/jfan.1997.3204
- Alexander J. Izzo, Uniform algebras generated by holomorphic and pluriharmonic functions, Trans. Amer. Math. Soc. 339 (1993), no. 2, 835–847. MR 1139494, DOI https://doi.org/10.1090/S0002-9947-1993-1139494-6
- James E. Thomson, The commutant of a class of analytic Toeplitz operators, Amer. J. Math. 99 (1977), no. 3, 522–529. MR 461196, DOI https://doi.org/10.2307/2373929
- James Thomson, The commutant of a class of analytic Toeplitz operators. II, Indiana Univ. Math. J. 25 (1976), no. 8, 793–800. MR 417843, DOI https://doi.org/10.1512/iumj.1976.25.25063
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Additional Information
Sheldon Axler
Affiliation:
Department of Mathematics, San Francisco State University, San Francisco, California 94132
MR Author ID:
201457
ORCID:
0000-0003-1733-6080
Email:
axler@sfsu.edu
Željko Čučković
Affiliation:
Department of Mathematics, University of Toledo, Toledo, Ohio 43606
MR Author ID:
294593
Email:
zcuckovi@math.utoledo.edu
N. V. Rao
Email:
rnagise@math.utoledo.edu
Received by editor(s):
August 8, 1998
Published electronically:
October 29, 1999
Additional Notes:
The first author was partially supported by the National Science Foundation
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000
American Mathematical Society
