Norm attaining bilinear forms on the plane with the l1-norm

Sung Guen Kim

doi:10.2478/ausm-2022-0008

Norm attaining bilinear forms on the plane with the l₁-norm

Sung Guen Kim

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

2 Scopus citations

Abstract

For given unit vectors x₁, · · ·, x_nof a real Banach space E, we define 'Equation Presented', where l(ⁿE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup ||x_k||=1,1≤k≤n |T(x1,⋯, xn)|. In this paper, we classify NA(L(²l²₁))((x1; x2); (y1; y2)) for unit vectors (x1; x2); (y1; y2) ∈ l²₁; where l²₁= ℝ²with the l₁-norm.

Original language	English
Pages (from-to)	115-124
Number of pages	10
Journal	Acta Universitatis Sapientiae, Mathematica
Volume	14
Issue number	1
DOIs	https://doi.org/10.2478/ausm-2022-0008
State	Published - 1 Nov 2022

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norm attaining bilinear forms

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10.2478/ausm-2022-0008

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abstract = "For given unit vectors x1, · · ·, xnof a real Banach space E, we define 'Equation Presented', where l(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup ||xk||=1,1≤k≤n |T(x1,⋯, xn)|. In this paper, we classify NA(L(2l21))((x1; x2); (y1; y2)) for unit vectors (x1; x2); (y1; y2) ∈ l21; where l21= ℝ2with the l1-norm.",

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AB - For given unit vectors x1, · · ·, xnof a real Banach space E, we define 'Equation Presented', where l(nE) denotes the Banach space of all continuous n-linear forms on E endowed with the norm ||T|| = sup ||xk||=1,1≤k≤n |T(x1,⋯, xn)|. In this paper, we classify NA(L(2l21))((x1; x2); (y1; y2)) for unit vectors (x1; x2); (y1; y2) ∈ l21; where l21= ℝ2with the l1-norm.

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Norm attaining bilinear forms on the plane with the l₁-norm

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