Extreme and exposed points of L(^n l^2_∞ ) and L_s (^n l^2_∞)

Authors

  • Sung Guen Kim Department of Mathematics, Kyungpook National University Daegu 702-701, South Korea

DOI:

https://doi.org/10.17398/2605-5686.35.2.127

Keywords:

n-linear forms, symmetric n-linear forms, extreme points, exposed points

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 l2∞ ) and Ls(n l2∞ ), where  L(n l2∞ ) is the space of n-linear forms on R2 with the supremum norm, and Ls(n l2∞ ) is the subspace of L(n l2∞ ) consisting of symmetric n-linear forms. First we classify the extreme points of the closed unit balls of L(n l2∞ ) and Ls(n l2∞ ) correspondingly. As corollaries we obtain |ext BL(n l2∞ ) | = 2(2n) and  =|ext BLs(n l2∞ ) | =2n+1. We also show that exp BL(n l2∞ ) =ext BL(n l2∞ ) and exp BLs(n l2∞ ) =ext BLs(n l2∞ ) .

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References

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Published

2020-12-01

Issue

Vol. 35 No. 2 (2020)

Section

Banach Spaces and Operator Theory

How to Cite

Extreme and exposed points of L(^n l^2_∞ ) and L_s (^n l^2_∞). (2020). Extracta Mathematicae, 35(2), 127-135. https://doi.org/10.17398/2605-5686.35.2.127