Extreme and exposed points of L(nl2 1 ) and Ls(nl2 ∞)

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(nl2 ∞) and Ls(nl2 ∞), where L(nl2 ∞) is the space of n-linear forms on R2 with the supremum norm, and Ls(nl2 ∞) is the subspace of L(nl2 ∞ ) consisting of symmetric n-linear forms. First we classify the extreme points of the closed unit balls of L(nl2 ∞) and Ls(nl2 ∞ ), correspondingly. As corollaries we obtain j extBL(nl2 ∞)j = 2(2n) and j extBLs(nl2 ∞)j = 2n+1. We also show that expBL(nl2 ∞) = extBL(nl2 ∞) and expBLs(nl2 ∞) = extBLs(nl2 ∞).