검색
Article Search

JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
QR Code

Published Online

Kyungpook Mathematical Journal

Published online July 14, 2020

Copyright © Kyungpook Mathematical Journal.

Extreme Points, Exposed Points and Smooth Points of the Space L s( 2𝑙3)

Sung Guen Kim

Department of Mathematics, Kyungpook National University, Daegu 41566, Repub- lic of Korea
e-mail : sgk317@knu.ac.kr

Received: September 5, 2019; Revised: March 10, 2020; Accepted: April 21, 2020

Abstract

We present a complete description of all the extreme points of the unit ball of L s( 2𝑙3) which leads to a complete formula for f for every 𝑓 L s( 2𝑙3)*. We also show that extB L s( 2𝑙3) extB L s( 2𝑙n) for every n ≥ 4. Using the formula for f for every f L s( 2𝑙3)*, we show that every extreme point of the unit ball of L s( 2𝑙3) is exposed. We also characterize all the smooth points of the unit ball of L s( 2𝑙3).

Keywords: symmetric bilinear forms on ℝ,3 with the supremum norm, extreme points, exposed points, smooth points