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

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∞ ) .