Exposed 2-homogeneous polynomials on Hilbert spaces

Sung Guen Kim; Sang Hun Lee

doi:10.1090/S0002-9939-02-06544-9

Exposed 2-homogeneous polynomials on Hilbert spaces

Sung Guen Kim, Sang Hun Lee

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

We show that every extreme point of the unit ball of 2-homogeneous polynomials on a separable real Hubert space is its exposed point and that the unit ball of 2-homogeneous polynomials on a non-separable real Hubert space contains no exposed points. We also show that the unit ball of 2-homogeneous polynomials on any infinite dimensional real Hubert space contains no strongly exposed points.

Original language	English
Pages (from-to)	449-453
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-02-06544-9
State	Published - Feb 2003

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AB - We show that every extreme point of the unit ball of 2-homogeneous polynomials on a separable real Hubert space is its exposed point and that the unit ball of 2-homogeneous polynomials on a non-separable real Hubert space contains no exposed points. We also show that the unit ball of 2-homogeneous polynomials on any infinite dimensional real Hubert space contains no strongly exposed points.

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Exposed 2-homogeneous polynomials on Hilbert spaces

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