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A remark on the geometry of the Gowers space

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Author(s): Luis A R Grados

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 24;
Issue: 1-2;
Start page: 35;
Date: 2006;
Original page

Keywords: Gowers | complex space | extreme points.

ABSTRACT
Let G_p be the Gowers complex space of characteristic p, B_p be theunitary 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.
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