Local properties of polynomials on a Banach space

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

Local properties of polynomials on a Banach space

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

Kent State University

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

15 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, L_p(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, L_p(μ) (1 ≤ p ≤ ∞), and C(K).

Original language	English
Pages (from-to)	25-39
Number of pages	15
Journal	Illinois Journal of Mathematics
Volume	45
Issue number	1
State	Published - Mar 2001

Cite this

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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).",

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N2 - 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).

AB - 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).

UR - https://www.scopus.com/pages/publications/0035276494

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Local properties of polynomials on a Banach space

Abstract

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