NORM-PEAK MULTILINEAR FORMS ON ℓ1

Sung Guen Kim

doi:10.56947/gjom.v16i1.1728

NORM-PEAK MULTILINEAR FORMS ON ℓ₁

Sung Guen Kim

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

Abstract

Let n ∈ N, n ≥ 2. A continuous n-linear form T on a Banach space E is called norm-peak if there is unique (x₁, …, x_n) ∈ Eⁿ such that ‖x₁‖ = · · · = ‖x_n‖ = 1 and T attains its norm only at (±x₁, …, ±x_n). In this paper, we characterize the norm-peak multilinear forms on ℓ₁.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Gulf Journal of Mathematics
Volume	16
Issue number	1
DOIs	https://doi.org/10.56947/gjom.v16i1.1728
State	Published - 2024

Keywords

norm-peak multilinear forms
Norming points

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10.56947/gjom.v16i1.1728

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abstract = "Let n ∈ N, n ≥ 2. A continuous n-linear form T on a Banach space E is called norm-peak if there is unique (x1, …, xn) ∈ En such that ‖x1‖ = · · · = ‖xn‖ = 1 and T attains its norm only at (±x1, …, ±xn). In this paper, we characterize the norm-peak multilinear forms on ℓ1.",

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AB - Let n ∈ N, n ≥ 2. A continuous n-linear form T on a Banach space E is called norm-peak if there is unique (x1, …, xn) ∈ En such that ‖x1‖ = · · · = ‖xn‖ = 1 and T attains its norm only at (±x1, …, ±xn). In this paper, we characterize the norm-peak multilinear forms on ℓ1.

KW - norm-peak multilinear forms

KW - Norming points

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NORM-PEAK MULTILINEAR FORMS ON ℓ₁

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