A characterization of compact perturbations of Toeplitz operators
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- by Jingbo Xia PDF
- Trans. Amer. Math. Soc. 361 (2009), 5163-5175 Request permission
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.References
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Additional Information
- Jingbo Xia
- Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
- MR Author ID: 215486
- Email: jxia@acsu.buffalo.edu
- 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.
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 5163-5175
- MSC (2000): Primary 47A55, 47B35
- DOI: https://doi.org/10.1090/S0002-9947-09-04736-9
- MathSciNet review: 2515807