The Norming Sets ofLml1n

Sung Guen Kim

doi:10.1007/s11253-024-02329-4

The Norming Sets ofLml1n

Sung Guen Kim

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

Abstract

Let n ∈ ℕ, n ≥ 2. An element (x₁,…,x_n) ∈ E_n is called a norming point of T ∈ LnE if ||x₁|| = … = ||x_n|| = 1 and |T(x₁,…,x_n)| = ||T||, where ℒ(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ (ⁿE), we define (Formula presented.) The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ Lml₁ⁿ, where l₁ⁿ=Rⁿ with the l₁-norm. As applications, we classify Norm(T) for every T ∈ Lml₁ⁿ with n = 2, 3 and m = 2.

Original language	English
Pages (from-to)	426-442
Number of pages	17
Journal	Ukrainian Mathematical Journal
Volume	76
Issue number	3
DOIs	https://doi.org/10.1007/s11253-024-02329-4
State	Published - Aug 2024

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title = "The Norming Sets ofLml1n",

abstract = "Let n ∈ ℕ, n ≥ 2. An element (x1,…,xn) ∈ En is called a norming point of T ∈ LnE if ||x1|| = … = ||xn|| = 1 and |T(x1,…,xn)| = ||T||, where ℒ(nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ (nE), we define (Formula presented.) The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ Lml1n, where l1n=Rn with the l1-norm. As applications, we classify Norm(T) for every T ∈ Lml1n with n = 2, 3 and m = 2.",

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N2 - Let n ∈ ℕ, n ≥ 2. An element (x1,…,xn) ∈ En is called a norming point of T ∈ LnE if ||x1|| = … = ||xn|| = 1 and |T(x1,…,xn)| = ||T||, where ℒ(nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ (nE), we define (Formula presented.) The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ Lml1n, where l1n=Rn with the l1-norm. As applications, we classify Norm(T) for every T ∈ Lml1n with n = 2, 3 and m = 2.

AB - Let n ∈ ℕ, n ≥ 2. An element (x1,…,xn) ∈ En is called a norming point of T ∈ LnE if ||x1|| = … = ||xn|| = 1 and |T(x1,…,xn)| = ||T||, where ℒ(nE) denotes the space of all continuous n-linear forms on E. For T ∈ ℒ (nE), we define (Formula presented.) The set Norm(T) is called the norming set of T. For m ∈ ℕ, m ≥ 2, we characterize Norm(T) for any T ∈ Lml1n, where l1n=Rn with the l1-norm. As applications, we classify Norm(T) for every T ∈ Lml1n with n = 2, 3 and m = 2.

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The Norming Sets ofLml1n

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