[Banach] Abstract of a paper by Sheng Zhang

This is an announcement for the paper "Coarse quotient mappings between metric spaces" by Sheng Zhang.

Abstract: We give a definition of coarse quotient mapping and show that several results for uniform quotient mapping also hold in the coarse setting. In particular, we prove that any Banach space that is a coarse quotient of $L_p\equiv L_p[0,1]$, $1<p<\infty$, is isomorphic to a linear quotient of $L_p$. It is also proved that $\ell_q$ is not a coarse quotient of $\ell_p$ for $1<p<q<\infty$ using Rolewicz's property ($\beta$).

Archive classification: math.FA math.MG

Submitted from: z1986s@math.tamu.edu

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

http://front.math.ucdavis.edu/1403.1934

or

http://arXiv.org/abs/1403.1934