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

 

Exposed 2-homogeneous polynomials on Hilbert spaces


Authors: Sung Guen Kim and Sang Hun Lee
Journal: Proc. Amer. Math. Soc. 131 (2003), 449-453
MSC (2000): Primary 46B20, 46E15
Published electronically: May 17, 2002
MathSciNet review: 1933336
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Abstract: We show that every extreme point of the unit ball of 2-homogene- ous polynomials on a separable real Hilbert space is its exposed point and that the unit ball of 2-homogeneous polynomials on a non-separable real Hilbert space contains no exposed points. We also show that the unit ball of 2-homogeneous polynomials on any infinite dimensional real Hilbert space contains no strongly exposed points.


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Additional Information

Sung Guen Kim
Affiliation: Department of Mathematics, Kyungpook National University, Daegu, Korea (702-701)
Email: sgk317@knu.ac.kr

Sang Hun Lee
Affiliation: Department of Mathematics, Kyungpook National University, Daegu, Korea (702-701)
Email: sanghlee@knu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06544-9
PII: S 0002-9939(02)06544-9
Received by editor(s): January 15, 2001
Received by editor(s) in revised form: September 10, 2001
Published electronically: May 17, 2002
Additional Notes: The first author wishes to acknowledge the financial support of the Korea Research Foundation (KRF-2000-015-DP0012)
The second author wishes to acknowledge the financial support by KOSEF research No. (2001-1-10100-007).
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society