THE NORMING SETS OF L(2 l21) and Ls (2 l31)

Sung Guen Kim

doi:10.31926/but.mif.2022.2.64.2.10

THE NORMING SETS OF L(² l²₁) and L_s (² l³₁)

Sung Guen Kim

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

8 Scopus citations

Abstract

Let n ∈ N. An element (x₁, …, x_n) ∈ Eⁿ is called a norming point of T ∈ L(ⁿ E) if ∥x₁ ∥ = · · · = ∥x_n ∥ = 1 and |T (x₁, …, x_n)| = ∥T ∥, where L(ⁿ E) denotes the space of all continuous n-linear forms on E. For T ∈ L(ⁿ E), we define Norm(T) = { (x₁, …, x_n) ∈ Eⁿ: (x₁, …, x_n) is a norming point of T } . Norm(T) is called the norming set of T . We classify Norm(T) for every T ∈ L(² l1)² or L_s (² l1),³ where l1ⁿ = Rⁿ with the l₁-norm.

Original language	English
Pages (from-to)	125-150
Number of pages	26
Journal	Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science
Volume	2
Issue number	2
DOIs	https://doi.org/10.31926/but.mif.2022.2.64.2.10
State	Published - 29 Dec 2022

Keywords

bilinear forms
Norming points

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10.31926/but.mif.2022.2.64.2.10

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title = "THE NORMING SETS OF L(2 l21) and Ls (2 l31)",

abstract = "Let n ∈ N. An element (x1, …, xn) ∈ En is called a norming point of T ∈ L(n E) if ∥x1 ∥ = · · · = ∥xn ∥ = 1 and |T (x1, …, xn)| = ∥T ∥, where L(n E) denotes the space of all continuous n-linear forms on E. For T ∈ L(n E), we define Norm(T) = \{ (x1, …, xn) ∈ En: (x1, …, xn) is a norming point of T \} . Norm(T) is called the norming set of T . We classify Norm(T) for every T ∈ L(2 l1)2 or Ls (2 l1),3 where l1n = Rn with the l1-norm.",

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N2 - Let n ∈ N. An element (x1, …, xn) ∈ En is called a norming point of T ∈ L(n E) if ∥x1 ∥ = · · · = ∥xn ∥ = 1 and |T (x1, …, xn)| = ∥T ∥, where L(n E) denotes the space of all continuous n-linear forms on E. For T ∈ L(n E), we define Norm(T) = { (x1, …, xn) ∈ En: (x1, …, xn) is a norming point of T } . Norm(T) is called the norming set of T . We classify Norm(T) for every T ∈ L(2 l1)2 or Ls (2 l1),3 where l1n = Rn with the l1-norm.

AB - Let n ∈ N. An element (x1, …, xn) ∈ En is called a norming point of T ∈ L(n E) if ∥x1 ∥ = · · · = ∥xn ∥ = 1 and |T (x1, …, xn)| = ∥T ∥, where L(n E) denotes the space of all continuous n-linear forms on E. For T ∈ L(n E), we define Norm(T) = { (x1, …, xn) ∈ En: (x1, …, xn) is a norming point of T } . Norm(T) is called the norming set of T . We classify Norm(T) for every T ∈ L(2 l1)2 or Ls (2 l1),3 where l1n = Rn with the l1-norm.

KW - bilinear forms

KW - Norming points

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THE NORMING SETS OF L(² l²₁) and L_s (² l³₁)

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