In this paper we show that a necessary and sufficient condition on a Banach space $B$ for the validity of the accompanying laws theorem is that $c_0$ is not finitely representable in $B$ or, equivalently, that $B$ is of cotype $q$ for some $q > 0$. The proof is based on a result of Maurey and Pisier on the geometry of these spaces and on a theorem about approximation in $L_p$ of Banach valued triangular arrays by finite dimensional ones.
Publié le : 1981-04-14
Classification:
Triangular arrays,
accompanying laws,
cotype,
finite representability of $c_0$,
60F05,
60B10,
46B99
@article{1176994462,
author = {Araujo, Aloisio and Gine, Evarist and Mandrekar, V. and Zinn, Joel},
title = {On the Accompanying Laws Theorem in Banach Spaces},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 202-210},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994462}
}
Araujo, Aloisio; Gine, Evarist; Mandrekar, V.; Zinn, Joel. On the Accompanying Laws Theorem in Banach Spaces. Ann. Probab., Tome 9 (1981) no. 6, pp. 202-210. http://gdmltest.u-ga.fr/item/1176994462/