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Title: | Extreme and exposed points of ℒ(^n ɭ^2_∞ ) and ℒs (^n ɭ^2_∞) |
Authors: | Kim, Sung Guen |
Keywords: | n-linear forms;Symmetric n-linear forms;Extreme points;Exposed points;Formas n-lineales;Formas n-lineales simétricas;Puntos extremos;Puntos expuestos |
Issue Date: | 2020 |
Publisher: | Universidad de Extremadura |
Abstract: | For every n ≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of ℒ(n ɭ2∞ ) and ℒs(n ɭ2∞ ), where ℒ(n ɭ2∞ ) is the space of n-linear forms on ℝ2 with the supremum norm, and ℒs(n ɭ2∞ ) is the subspace of ℒ(n ɭ2∞ ) consisting of symmetric n-linear forms. First we classify the extreme points of the closed unit balls of ℒ(n ɭ2∞ ) and ℒs(n ɭ2∞ ) correspondingly. As corollaries we obtain |ext Bℒ(n ɭ2∞ ) | = 2(2n) and =|ext Bℒs(n ɭ2∞ ) | =2n+1. We also show that exp BL(n ɭ2∞ ) =ext Bℒ(n ɭ2∞ ) and exp Bℒs(n ɭ2∞ ) =ext Bℒs(n ɭ2∞ ) . |
URI: | http://hdl.handle.net/10662/12284 |
DOI: | 10.17398/2605-5686.35.2.127 |
Appears in Collections: | Extracta Mathematicae Vol. 35, nº 2 (2020) |
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