Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-02-06544-9
Published electronically: May 17, 2002
MathSciNet review: 1933336
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. C. Boyd and R.A. Ryan, Geometric theory of spaces of integral polynomials and symmetric tensor products, J. Funct. Anal. 179 (2001), 18-42. MR 2002b:46029
  • 2. Y.S. Choi, H. Ki and S.G. Kim, Extreme polynomials and multilinear forms on $l_1$, J. Math. Anal. Appl. 228 (1998), 467-482. MR 99k:46077b
  • 3. Y.S. Choi and S.G. Kim, The unit ball of ${\mathcal P}(^2l_2^2)$, Arch. Math. 71 (1998), 472-480. MR 2000c:46085
  • 4. Y.S. Choi and S.G. Kim, Exposed points of the unit balls of ${\mathcal P}(^2l_p^2)$ $(p=1, 2, \infty)$, (Preprint).
  • 5. S. Dineen, Extreme integral polynomials on a complex Banach space, (Preprint).
  • 6. B.C. Grecu, Extreme polynomials on Hilbert spaces, (Preprint).
  • 7. R.A. Ryan and B. Turett, Geometry of spaces of polynomials, J. Math. Anal. Appl. 221 (1998), 698-711. MR 99g:46015

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46B20, 46E15

Retrieve articles in all journals with MSC (2000): 46B20, 46E15


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: https://doi.org/10.1090/S0002-9939-02-06544-9
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

American Mathematical Society