Extreme bilinear forms on Rn with the supremum norm

For every n = 2 this paper is devoted to the description of the sets of extreme points of the closed unit balls of L(2ln8) and Ls (2ln8), where L(2ln8) is the space of bilinear forms on Rn with the supremum norm, and Ls (2ln8) is the subspace of L(2ln8) consisting of symmetric bilinear forms. First we obtain an elegant formula for calculating the norm of a given bilinear form T. L(2ln8). We present a characterization of the sets ext BL(2ln8) and ext BLs (2ln8), correspondingly. We obtain a sufficient condition for a given bilinear form T. ext BLs (2ln8) to be considered as an element of ext BLs (2ln+ 1 8). As applications we show that for every n = 3 the relations ext BL(2l28). ext BL(2ln8) and ext BLs (2l28). ext BLs (2ln8) hold true. In addition it is shown that for n = 3, ext BLs (2ln8) . ext BL(2ln8) in contrast to the case n = 2.