The unit balls of ℒ(nl∞m) and ℒs(nl∞m)

Abstract

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 and , where is the space of n-linear forms on with the supremum norm, and is the subspace of consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of and , respectively. We show that ext ⊂ ext , which answers the question in [32]. We show that every extreme point of the unit balls of and is exposed, correspondingly. We also show thatand which answers the questions in [31].