%0 Journal Article
%T Property $(¦Â)$ and uniform quotient maps
%A Vegard Lima
%A N. Lovasoa Randrianarivony
%J Mathematics
%D 2010
%I arXiv
%X In 1999, Bates, Johnson, Lindenstrauss, Preiss and Schechtman asked whether a Banach space that is a uniform quotient of $\ell_p$, $1 < p \neq 2 < \infty$, must be isomorphic to a linear quotient of $\ell_p$. We apply the geometric property $(\beta)$ of Rolewicz to the study of uniform and Lipschitz quotient maps, and answer the above question positively for the case $1<p<2$. We also give a necessary condition for a Banach space to have $c_0$ as a uniform quotient.
%U http://arxiv.org/abs/1010.0184v1