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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A characterization of compact perturbations of Toeplitz operators


Author: Jingbo Xia
Journal: Trans. Amer. Math. Soc. 361 (2009), 5163-5175
MSC (2000): Primary 47A55, 47B35
Published electronically: April 7, 2009
MathSciNet review: 2515807
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Abstract: Let $ X$ be a bounded operator on the Hardy space $ H^{2}$ of the unit circle. It has been a longstanding problem to determine whether the condition that $ T_{\bar u}XT_{u} - X$ is compact for every inner function $ u$ implies that $ X$ is a compact perturbation of a Toeplitz operator. We show that the answer is affirmative.


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Additional Information

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: jxia@acsu.buffalo.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04736-9
PII: S 0002-9947(09)04736-9
Received by editor(s): August 20, 2007
Published electronically: April 7, 2009
Additional Notes: This work was supported by National Science Foundation grant DMS-0456448.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.