[Banach] Abstract of a paper by Vegard Lima and N. Lovasoa Randrianarivony

This is an announcement for the paper "Property $(\beta)$ and uniform quotient maps" by Vegard Lima and N. Lovasoa Randrianarivony.

Abstract: 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.

Archive classification: math.FA math.MG

Submitted from: nrandria@slu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1010.0184

or

http://arXiv.org/abs/1010.0184