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Strict convexity of some subsets of Hankel operators
Author(s):
Caixing
Gu;
Jonathan
E.
Shapiro
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2779-2789.
MSC (2000):
Primary 47B35, 47B20
Posted:
January 2, 2003
MathSciNet review:
1974335
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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  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
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:
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
Posted:
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 of article:
Copyright
2003,
by the authors
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