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arXiv · 1010.0184

Property $(β)$ and uniform quotient maps

Vegard Lima·N. Lovasoa Randrianarivony
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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 $(β)$ 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.

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Vegard Lima, N. Lovasoa Randrianarivony. 2010-10-01. Property $(β)$ and uniform quotient maps. https://arxiv.org/abs/1010.0184

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