Geometry of bilinear forms on the plane with hexagonal norms

Sung Guen Kim

Geometry of bilinear forms on the plane with hexagonal norms

Sung Guen Kim

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

Abstract

Let 0 < w₁, w₂ < 1. We denote by R²_h(w1,w2)the plane with the hexagonal norm ∥(x, y)∥_h(w1,w2)= max { |y|, w₁ |x| + w₂ |y|}. We denote by R²_{h′ (w1,w2)} the plane with the hexagonal norm ∥(x, y)∥_{h′ (w1,w2)}= max {|x|, w₁ |x| + w₂ |y|}. In this paper, we classify the extreme bilinear forms of the unit balls of L(²X) and L_s(²X), where X = R²_h(w1,w2)or R²_h′(w1,w2). From this, we induce that ext B_Ls(²X) = ext B_L(²X) ∩ L_s(²X). We show that every extreme bilinear forms on that spaces is exposed.

Original language	English
Pages (from-to)	553-570
Number of pages	18
Journal	Palestine Journal of Mathematics
Volume	13
Issue number	3
State	Published - 2024

Keywords

Bilinear forms
exposed points
extreme points
hexagonal norms on the plane

Cite this

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title = "Geometry of bilinear forms on the plane with hexagonal norms",

abstract = "Let 0 < w1, w2 < 1. We denote by R2h(w1,w2)the plane with the hexagonal norm ∥(x, y)∥h(w1,w2)= max \{ |y|, w1 |x| + w2 |y|\}. We denote by R2h′ (w1,w2) the plane with the hexagonal norm ∥(x, y)∥h′ (w1,w2)= max \{|x|, w1 |x| + w2 |y|\}. In this paper, we classify the extreme bilinear forms of the unit balls of L(2X) and Ls(2X), where X = R2h(w1,w2)or R2h′(w1,w2). From this, we induce that ext BLs(2X) = ext BL(2X) ∩ Ls(2X). We show that every extreme bilinear forms on that spaces is exposed.",

keywords = "Bilinear forms, exposed points, extreme points, hexagonal norms on the plane",

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T1 - Geometry of bilinear forms on the plane with hexagonal norms

AU - Kim, Sung Guen

N1 - Publisher Copyright: © Palestine Polytechnic University-PPU 2024.

PY - 2024

Y1 - 2024

N2 - Let 0 < w1, w2 < 1. We denote by R2h(w1,w2)the plane with the hexagonal norm ∥(x, y)∥h(w1,w2)= max { |y|, w1 |x| + w2 |y|}. We denote by R2h′ (w1,w2) the plane with the hexagonal norm ∥(x, y)∥h′ (w1,w2)= max {|x|, w1 |x| + w2 |y|}. In this paper, we classify the extreme bilinear forms of the unit balls of L(2X) and Ls(2X), where X = R2h(w1,w2)or R2h′(w1,w2). From this, we induce that ext BLs(2X) = ext BL(2X) ∩ Ls(2X). We show that every extreme bilinear forms on that spaces is exposed.

AB - Let 0 < w1, w2 < 1. We denote by R2h(w1,w2)the plane with the hexagonal norm ∥(x, y)∥h(w1,w2)= max { |y|, w1 |x| + w2 |y|}. We denote by R2h′ (w1,w2) the plane with the hexagonal norm ∥(x, y)∥h′ (w1,w2)= max {|x|, w1 |x| + w2 |y|}. In this paper, we classify the extreme bilinear forms of the unit balls of L(2X) and Ls(2X), where X = R2h(w1,w2)or R2h′(w1,w2). From this, we induce that ext BLs(2X) = ext BL(2X) ∩ Ls(2X). We show that every extreme bilinear forms on that spaces is exposed.

KW - Bilinear forms

KW - exposed points

KW - extreme points

KW - hexagonal norms on the plane

UR - https://www.scopus.com/pages/publications/85207673072

M3 - Article

AN - SCOPUS:85207673072

SN - 2219-5688

VL - 13

SP - 553

EP - 570

JO - Palestine Journal of Mathematics

JF - Palestine Journal of Mathematics

IS - 3

ER -

Geometry of bilinear forms on the plane with hexagonal norms

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Keywords

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