International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 43875, 12 pages

Weak Grothendieck's theorem

Lahcène Mezrag

Department of Mathematics, M'sila University, P.O. Box 166, M'sila 28000, Algeria

Received 14 June 2005; Revised 9 March 2006; Accepted 20 June 2006

Copyright © 2006 Lahcène Mezrag. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.