The norming sets of L(2Rh(w)2)

Sung Guen Kim

doi:10.1007/s44146-023-00078-7

The norming sets of L⁽²Rh(w)2)

Sung Guen Kim

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

7 Scopus citations

Abstract

An element (x₁, … , x_n) ∈ Eⁿ is called a norming point of T∈ L(ⁿE) 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 Norm(T)={(x1,…,xn)∈En:(x1,…,xn)isanormingpointofT}. Let Rh(w)2 denote the plane with the hexagonal norm with weight 0 < w< 1 ‖(x,y)‖h(w)=max{|y|,|x|+(1-w)|y|}. We classify Norm (T) for every T∈L(2Rh(w)2) .

Original language	English
Pages (from-to)	61-79
Number of pages	19
Journal	Acta Scientiarum Mathematicarum
Volume	89
Issue number	1-2
DOIs	https://doi.org/10.1007/s44146-023-00078-7
State	Published - Jun 2023

Keywords

Bilinear forms
Norming points

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10.1007/s44146-023-00078-7

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title = "The norming sets of L(2Rh(w)2)",

abstract = "An element (x1, … , xn) ∈ En is called a norming point of T∈ L(nE) 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 Norm(T)=\{(x1,…,xn)∈En:(x1,…,xn)isanormingpointofT\}. Let Rh(w)2 denote the plane with the hexagonal norm with weight 0 < w< 1 ‖(x,y)‖h(w)=max\{|y|,|x|+(1-w)|y|\}. We classify Norm (T) for every T∈L(2Rh(w)2) .",

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N2 - An element (x1, … , xn) ∈ En is called a norming point of T∈ L(nE) 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 Norm(T)={(x1,…,xn)∈En:(x1,…,xn)isanormingpointofT}. Let Rh(w)2 denote the plane with the hexagonal norm with weight 0 < w< 1 ‖(x,y)‖h(w)=max{|y|,|x|+(1-w)|y|}. We classify Norm (T) for every T∈L(2Rh(w)2) .

AB - An element (x1, … , xn) ∈ En is called a norming point of T∈ L(nE) 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 Norm(T)={(x1,…,xn)∈En:(x1,…,xn)isanormingpointofT}. Let Rh(w)2 denote the plane with the hexagonal norm with weight 0 < w< 1 ‖(x,y)‖h(w)=max{|y|,|x|+(1-w)|y|}. We classify Norm (T) for every T∈L(2Rh(w)2) .

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KW - Norming points

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The norming sets of L⁽²Rh(w)2)

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