Separation for kernels of Hankel operators
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- by Caixing Gu PDF
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Abstract:
We prove that for two Hankel operators $H_{a_{1}}$ and $H_{a_{2}}$ on the Hardy space of the unit disk either the kernel of $H_{a_{1}}^{*}H_{a_{2}}$ equals the kernel of $H_{a_{2}}$ or the kernel of $H_{a_{2}}^{*}H_{a_{1}}$ equals the kernel of $H_{a_{1}}$. In fact we prove a version of the above result for products of an arbitrary finite number of Hankel operators. Some immediate corollaries are generalizations of the result of Brown and Halmos on zero products of two Hankel operators and the result of Axler, Chang and Sarason on finite rank products of two Hankel operators. Simple examples show our results are sharp.References
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Additional Information
- Caixing Gu
- Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
- MR Author ID: 236909
- ORCID: 0000-0001-6289-7755
- Email: cgu@calpoly.edu
- Received by editor(s): May 4, 1999
- Received by editor(s) in revised form: December 7, 1999
- Published electronically: December 28, 2000
- Additional Notes: This research was partially supported by the National Science Foundation Grant DMS-9706838 and the SFSG Grant of California Polytechnic State University.
- Communicated by: Joseph A. Ball
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2353-2358
- MSC (2000): Primary 47B35
- DOI: https://doi.org/10.1090/S0002-9939-00-05807-X
- MathSciNet review: 1823918