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There are no denting points in the unit ball of 𝒫(2H)

Published online by Cambridge University Press:  17 April 2009

Sung Guen Kim
Sung Guen Kim
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu (702–701), Korea e-mail: sgk317@knu.ac.kr
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For any infinite dimensional real Hilbert space H we show that the unit ball of the space of continuous 2-homogeneous polynomials on H, 𝒫(2H), has no denting points. Thus the unit ball of 𝒫(2H) has no strongly exposed points.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 497 - 498
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Dineen, S., Complex analysis on infinite dimensional spaces, Springer Monographs in Mathematics (Springer-Verlag, London, 1999).CrossRefGoogle Scholar
[2]Grecu, B.C., ‘Extreme polynomials on Hilbert spaces’, (preprint).Google Scholar
[3]Kim, S.G. and Lee, S.H., ‘Exposed 2-homogeneous polynomials on Hilbert spaces’, Proc. Amer. Math. Soc. (to appear).Google Scholar
[4]Rao, T.S.S.R.K., ‘There are no denting points in the unit ball of W C (K, X)’, Proc. Amer. Math. Soc. 127 (1999), 2969–2973.CrossRefGoogle Scholar