The Norming Set of a Bilinear Form on R2 with the Octagonal Norm

Sung Guen Kim; Chang Yeol Lee; Ukje Jeong

The Norming Set of a Bilinear Form on R² with the Octagonal Norm

Sung Guen Kim
, Chang Yeol Lee
, Ukje Jeong

Kyungpook National University

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

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, . . ., x_n) ∈ Eⁿ : (x₁, . . ., x_n) is a norming point of T}. Let R²_o(w) denote R² with the octagonal norm with weight 0 < w ≠ 1 ∥(x, y)∥_o(w) = max n |x| + w|y|, |y| + w|x| ^o . In this paper we classify Norm (T) for every T ∈ L(²R²_o(w)) with weight 0 < w ≠ 1.

Original language	English
Pages (from-to)	111-130
Number of pages	20
Journal	Journal of Convex Analysis
Volume	30
Issue number	1
State	Published - 2023

Keywords

bilinear forms
Norming points

Cite this

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title = "The Norming Set of a Bilinear Form on R2 with the Octagonal Norm",

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) is a norming point of T\}. Let R2o(w) denote R2 with the octagonal norm with weight 0 < w ≠ 1 ∥(x, y)∥o(w) = max n |x| + w|y|, |y| + w|x| o . In this paper we classify Norm (T) for every T ∈ L(2R2o(w)) with weight 0 < w ≠ 1.",

keywords = "bilinear forms, Norming points",

author = "Kim, \{Sung Guen\} and Lee, \{Chang Yeol\} and Ukje Jeong",

note = "Publisher Copyright: {\textcopyright} Heldermann Verlag.",

year = "2023",

language = "English",

volume = "30",

pages = "111--130",

journal = "Journal of Convex Analysis",

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T1 - The Norming Set of a Bilinear Form on R2 with the Octagonal Norm

AU - Kim, Sung Guen

AU - Lee, Chang Yeol

AU - Jeong, Ukje

N1 - Publisher Copyright: © Heldermann Verlag.

PY - 2023

Y1 - 2023

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) is a norming point of T}. Let R2o(w) denote R2 with the octagonal norm with weight 0 < w ≠ 1 ∥(x, y)∥o(w) = max n |x| + w|y|, |y| + w|x| o . In this paper we classify Norm (T) for every T ∈ L(2R2o(w)) with weight 0 < w ≠ 1.

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) is a norming point of T}. Let R2o(w) denote R2 with the octagonal norm with weight 0 < w ≠ 1 ∥(x, y)∥o(w) = max n |x| + w|y|, |y| + w|x| o . In this paper we classify Norm (T) for every T ∈ L(2R2o(w)) with weight 0 < w ≠ 1.

KW - bilinear forms

KW - Norming points

UR - https://www.scopus.com/pages/publications/85178340403

M3 - Article

AN - SCOPUS:85178340403

SN - 0944-6532

VL - 30

SP - 111

EP - 130

JO - Journal of Convex Analysis

JF - Journal of Convex Analysis

IS - 1

ER -

The Norming Set of a Bilinear Form on R² with the Octagonal Norm

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