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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Strict convexity of some subsets of Hankel operators


Authors: Caixing Gu and Jonathan E. Shapiro
Journal: Proc. Amer. Math. Soc. 131 (2003), 2779-2789
MSC (2000): Primary 47B35, 47B20
Published electronically: January 2, 2003
MathSciNet review: 1974335
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Caixing Gu
Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
Email: cgu@calpoly.edu

Jonathan E. Shapiro
Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
Email: jshapiro@calpoly.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06873-4
PII: S 0002-9939(03)06873-4
Keywords: Hankel operator, Toeplitz operator, convex
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
Article copyright: © Copyright 2003 by the authors