Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2019; 34(2): 487-494

Online first article October 18, 2018      Printed April 30, 2019

https://doi.org/10.4134/CKMS.c180111

Copyright © The Korean Mathematical Society.

The unit ball of the space of bilinear forms on $\mathbb{R}^3$ with the supremum norm

Sung Guen Kim

Kyungpook National University

Abstract

We classify all the extreme and exposed bilinear forms of the unit ball of ${\mathcal L}(^2l_{\infty}^3)$ which leads to a complete formula of $\|f\|$ for every $f\in {{\mathcal L}(^2l_{\infty}^3)}^*$. It follows from this formula that every extreme bilinear form of the unit ball of ${\mathcal L}(^2l_{\infty}^3)$ is exposed.

Keywords: bilinear forms on $\mathbb{R}^3$, extreme points, exposed points

MSC numbers: Primary 46A22