Abstract

Let EnL12n be the n-dimensional subspace which appeared in Kašin's theorem such that L12n=EnEn and the L12n and L22n norms are universally equivalent on both En and En. In this paper, we introduce and study some properties concerning extension and weak Grothendieck's theorem (WGT). We show that the Schatten space Sp for all 0<p does not verify the theorem of extension. We prove also that Sp fails GT for all 1p and consequently by one result of Maurey does not satisfy WGT for 1p2. We conclude by giving a characterization for spaces verifying WGT.