Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

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
MathSciNet review: 1933336
Retrieve article in: PDF
This article is available free of charge

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:

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 , 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: 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

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|