Local properties of polynomials on a Banach space

Richard M. Aron, Yun Sung Choi, Sung Guen Kim, Manuel Maestre

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We introduce the concept of a smooth point of order n of the closed unit ball of a Banach space E and characterize such points for E = c0, Lp(μ) (1 ≤ p ≤ ∞), and C(K). We show that every locally uniformly rotund multilinear form and homogeneous polynomial on a Banach space E is generated by locally uniformly rotund linear functionals on E. We also classify such points for E = c0, Lp(μ) (1 ≤ p ≤ ∞), and C(K).

Original languageEnglish
Pages (from-to)25-39
Number of pages15
JournalIllinois Journal of Mathematics
Volume45
Issue number1
StatePublished - Mar 2001

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