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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Exposed 2-homogeneous polynomials on Hilbert spaces
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by Sung Guen Kim and Sang Hun Lee PDF
Proc. Amer. Math. Soc. 131 (2003), 449-453 Request permission

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
  • 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