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Extreme Polynomials and Multilinear Forms onl1

✍ Scribed by Yun Sung Choi; Sung Guen Kim; Haseo Ki

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
125 KB
Volume
228
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

Given a 2-homogeneous polynomial P x, y s ax q by q cxy with real coeffi-5 5 5 5 cients, let P and P denote the norms of P on the real and complex Banach r c 2 5 5 5 5 space l , respectively. We show P s P , and obtain a sufficient and necessary r c 1 condition on the coefficients a, b, and c for P to have norm 1. Applying these Ž 2 . results, we characterize extreme points of the unit ball of P P l for the real 1 Banach space l 2 and examine them for the complex Banach space l 2 . We apply 1 1

Ž 2 . them to find extreme points and strongly extreme points of the unit ball of P P l 1 and get an extremal 2-homogeneous polynomial on l that is not an extreme point.

1

We also characterize extreme points and strongly extreme points of the unit ball of Ž m . Ž m w x.

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