Exposed 2-homogeneous polynomials on Hilbert spaces

Kim, Sung Guen; Lee, Sang Hun

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

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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