Strict convexity of some subsets of Hankel operators
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- by Caixing Gu and Jonathan E. Shapiro PDF
- Proc. Amer. Math. Soc. 131 (2003), 2779-2789
Abstract:
We find some extreme points in the unit ball of the set of Hankel operators and show that the unit ball of the set of compact Hankel operators is strictly convex. We use this result to show that the collection of $N\times N$ lower triangular Toeplitz contractions is strictly convex. We also find some extreme points in certain reduced Cowen sets and discuss cases in which they are or are not strictly convex.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
- Jonathan E. Shapiro
- Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
- MR Author ID: 622125
- Email: jshapiro@calpoly.edu
- Received by editor(s): October 10, 2001
- Received by editor(s) in revised form: April 1, 2002
- Published electronically: January 2, 2003
- Additional Notes: The work of the first author was partially supported by the National Science Foundation Grant DMS-0075127 and both authors were supported by the SFSG Grants of California Polytechnic State University.
- Communicated by: Joseph A. Ball
- © Copyright 2003 by the authors
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2779-2789
- MSC (2000): Primary 47B35, 47B20
- DOI: https://doi.org/10.1090/S0002-9939-03-06873-4
- MathSciNet review: 1974335