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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a problem of Axler, Cuckovic and Rao


Author: Guangfu Cao
Journal: Proc. Amer. Math. Soc. 136 (2008), 931-935
MSC (2000): Primary 47B35
Published electronically: November 23, 2007
MathSciNet review: 2361866
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Abstract: In this note we show that if two Toeplitz operators on a Bergman space of the (Levi) pseudoconvex domain commute and the symbol of one of them is analytic and non-constant, then the other one is also analytic. This gives an affirmative answer of a problem of S. Axler, Z. Cuckovic and N. V. Rao (1999).


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Additional Information

Guangfu Cao
Affiliation: Department of Mathematics, Guangzhou University, Guangzhou 510006, People’s Republic of China
Email: guangfucao@163.com

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08987-3
PII: S 0002-9939(07)08987-3
Keywords: Toeplitz operator, commutant of an operator
Received by editor(s): August 17, 2006
Received by editor(s) in revised form: October 31, 2006
Published electronically: November 23, 2007
Additional Notes: Supported by National Natural Science Foundation of China
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society