International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 43875, 12 pages
Weak Grothendieck's theorem
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 be the -dimensional subspace which appeared in Kašin's theorem such that and the and
norms are universally equivalent on both and . In this paper, we introduce and study some
properties concerning extension and weak Grothendieck's theorem
(WGT). We show that the Schatten space for all does not verify the theorem of extension. We prove
also that fails GT for all and consequently by one result of Maurey does not satisfy WGT for
. We conclude by giving a characterization for
spaces verifying WGT.