International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 13, Article ID 43875, 12 pages
doi:10.1155/IJMMS/2006/43875

Weak Grothendieck's theorem

Abstract

Let En⊂L12n be the n-dimensional subspace which appeared in Kašin's theorem such that L12n=En⊕En⊥ 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 1≤p≤∞ and consequently by one result of Maurey does not satisfy WGT for 1≤p≤2. We conclude by giving a characterization for spaces verifying WGT.