Extreme Polynomials and Multilinear Forms onl1

Yun Sung Choi, Sung Guen Kim, Haseo Ki

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Given a 2-homogeneous polynomialP(x,y)=ax2+by2+cxywith real coefficients, let Prand Pcdenote the norms ofPon the real and complex Banach spacel21, respectively. We show Pr=Pc, and obtain a sufficient and necessary condition on the coefficientsa,b, andcforPto have norm 1. Applying these results, we characterize extreme points of the unit ball of P(2l1) for the real Banach spacel21and examine them for the complex Banach spacel21. We apply them to find extreme points and strongly extreme points of the unit ball of P(2l1) and get an extremal 2-homogeneous polynomial onl1that is not an extreme point. We also characterize extreme points and strongly extreme points of the unit ball of L(ml1) or L(mL1[0,1]).

Original languageEnglish
Pages (from-to)467-482
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume228
Issue number2
DOIs
Publication statusPublished - 1998 Dec 15

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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