A remark on the geometry of the Gowers space - doi: 10.5269/bspm.v24i1-2.7438

Abstract

Let G_p be the Gowers complex space of characteristic p, B_p be the unitary closed ball and S_p be the unitary sphere of G_p. Then, any x \in B_p can be written in a unique form as the sum of an element of the torus and an element of the unitary open ball of the Gowers space of characteristic p + k, for some k \in N, which permit us to show that B_p does not have complex extreme points.