Exposed 2-homogeneous polynomials on Hilbert spaces
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- by Sung Guen Kim and Sang Hun Lee
- Proc. Amer. Math. Soc. 131 (2003), 449-453
- DOI: https://doi.org/10.1090/S0002-9939-02-06544-9
- Published electronically: 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.References
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Bibliographic 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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 449-453
- MSC (2000): Primary 46B20, 46E15
- DOI: https://doi.org/10.1090/S0002-9939-02-06544-9
- MathSciNet review: 1933336