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arXiv · 1403.1934

Coarse Quotient Mappings between Metric Spaces

Sheng Zhang
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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 ($β$).

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Sheng Zhang. 2014-03-08. Coarse Quotient Mappings between Metric Spaces. https://arxiv.org/abs/1403.1934

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