The unit balls of L(^nlm_∞) and L_s(^nlm_∞)

L(nlm∞) and Ls(nlm∞) For n,m ≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of L(nlm∞) and Ls(nlm∞) where L(nlm∞) is the space of n-linear forms on Rm with the supremum norm, and Ls(nlm∞) is the subspace of L(nlm∞) consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of L(nlm∞) and Ls(nlm∞), respectively. We show that ext BL(nlm∞) ⊂ ext BL(nlm+1∞) which answers the question in [32]. We show that every extreme point of the unit balls of L(nlm∞) and Ls(nlm∞) is exposed, correspondingly. We also show that (Equation Presented) and (Equation Presented) which answers the questions in [31].