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Exposed 2-homogeneous polynomials on Hilbert spaces

Author(s): Sung Guen Kim; Sang Hun Lee
Journal: Proc. Amer. Math. Soc. 131 (2003), 449-453.
MSC (2000): Primary 46B20, 46E15
Posted: May 17, 2002
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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: 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
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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The following works have cited this article

Sung Guen Kim, There are no denting points in the unit ball of $P(^2H)$, Bull. Austral. Math. Soc. 66 (2002), 497-498.

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