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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 operators which commute with analytic Toeplitz operators modulo the finite rank operators


Authors: Kunyu Guo and Kai Wang
Journal: Proc. Amer. Math. Soc. 134 (2006), 2571-2576
MSC (2000): Primary 47B35, 47B20
Published electronically: February 17, 2006
MathSciNet review: 2213734
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Abstract: It is shown that an operator $ S$ on the Hardy space $ H^2({\mathbb{D}}^n)$ (or $ H^2({\mathbb{B}}_n)$) commutes with all analytic Toeplitz operators modulo the finite rank operators if and only if $ S=T_g+F$. Here $ F$ is a finite rank operator, and in the case $ n=1$, $ g$ is a sum of a rational function and a bounded analytic function, and in the case $ n\geq 2$, $ g$ is a bounded analytic function.


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Additional Information

Kunyu Guo
Affiliation: School of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: kyguo@fudan.edu.cn

Kai Wang
Affiliation: School of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: 031018009@fudan.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08259-1
PII: S 0002-9939(06)08259-1
Keywords: Hardy space, Toeplitz operator, finite rank operator
Received by editor(s): December 13, 2004
Received by editor(s) in revised form: March 18, 2005
Published electronically: February 17, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.