GEOMETRY OF BILINEAR FORMS ON THE PLANE WITH THE OCTAGONAL NORM

Sung Guen Kim

doi:10.31926/but.mif.2021.1.63.1.12

GEOMETRY OF BILINEAR FORMS ON THE PLANE WITH THE OCTAGONAL NORM

Sung Guen Kim

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

1 Scopus citations

Abstract

Let R²o(w) be the plane with the octagonal norm with weight 0 < w, w ≠ 1 { } ‖(x, y)‖_o(w) = max |x| + w|y|, |y| + w|x|. In this paper we classify all extreme, exposed and smooth points of the closed unit balls of L(²R²o(w)^{) and L}s(²R²o(w)^{),where L(2}R²o(w)) is the space of bilinear forms on R²o(w)^{,and L}s(²R²o(w)^{) is the subspace of L(2}l∞,θ^{2) consisting} of symmetric bilinear forms.

Original language	English
Pages (from-to)	161-190
Number of pages	30
Journal	Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science
Volume	1
Issue number	1
DOIs	https://doi.org/10.31926/but.mif.2021.1.63.1.12
State	Published - 8 Oct 2021

Keywords

Exposed points
Extreme points
Smooth points

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title = "GEOMETRY OF BILINEAR FORMS ON THE PLANE WITH THE OCTAGONAL NORM",

abstract = "Let R2o(w) be the plane with the octagonal norm with weight 0 < w, w ≠ 1 { } ‖(x, y)‖o(w) = max |x| + w|y|, |y| + w|x|. In this paper we classify all extreme, exposed and smooth points of the closed unit balls of L(2R2o(w)) and Ls(2R2o(w)),where L(2R2o(w)) is the space of bilinear forms on R2o(w),and Ls(2R2o(w)) is the subspace of L(2l∞,θ2) consisting of symmetric bilinear forms.",

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N2 - Let R2o(w) be the plane with the octagonal norm with weight 0 < w, w ≠ 1 { } ‖(x, y)‖o(w) = max |x| + w|y|, |y| + w|x|. In this paper we classify all extreme, exposed and smooth points of the closed unit balls of L(2R2o(w)) and Ls(2R2o(w)),where L(2R2o(w)) is the space of bilinear forms on R2o(w),and Ls(2R2o(w)) is the subspace of L(2l∞,θ2) consisting of symmetric bilinear forms.

AB - Let R2o(w) be the plane with the octagonal norm with weight 0 < w, w ≠ 1 { } ‖(x, y)‖o(w) = max |x| + w|y|, |y| + w|x|. In this paper we classify all extreme, exposed and smooth points of the closed unit balls of L(2R2o(w)) and Ls(2R2o(w)),where L(2R2o(w)) is the space of bilinear forms on R2o(w),and Ls(2R2o(w)) is the subspace of L(2l∞,θ2) consisting of symmetric bilinear forms.

KW - Exposed points

KW - Extreme points

KW - Smooth points

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SN - 2810-2029

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JO - Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science

JF - Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science

IS - 1

ER -

GEOMETRY OF BILINEAR FORMS ON THE PLANE WITH THE OCTAGONAL NORM

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