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.
@article{7438, title = {A remark on the geometry of the Gowers space - doi: 10.5269/bspm.v24i1-2.7438}, journal = {Boletim da Sociedade Paranaense de Matem\'atica}, volume = {23}, year = {2009}, doi = {10.5269/bspm.v24i1-2.7438}, language = {EN}, url = {http://dml.mathdoc.fr/item/7438} }
Grados, Luis A. R. A remark on the geometry of the Gowers space - doi: 10.5269/bspm.v24i1-2.7438. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v24i1-2.7438. http://gdmltest.u-ga.fr/item/7438/