On uniform and coarse rigidity of $L^p([0,1])$

Christian Rosendal

On uniform and coarse rigidity of $L^p([0,1])$

Functional Analysis 2022-08-03 v2

Authors: Christian Rosendal

Abstract

If $X$ is an almost transitive Banach space with amenable isometry group (for example, if $X=L^p([0,1])$ with $1\leqslant p<\infty$ ) and $X$ admits a uniformly continuous map $X\overset\phi\longrightarrow E$ into a Banach space $E$ satisfying $\inf_{\|x-y\|=r} \| \phi(x)-\phi(y)\|>0$ for some $r>0$ , then $X$ admits a simultaneously uniform and coarse embedding into a Banach space $V$ that is finitely representable in $L^2(E)$ .

Keywords

banach space almost transitive amenable isometry group uniform embedding coarse embedding finitely representable l^p spaces

Cite

@article{arxiv.2206.01893,
  title  = {On uniform and coarse rigidity of $L^p([0,1])$},
  author = {Christian Rosendal},
  journal= {arXiv preprint arXiv:2206.01893},
  year   = {2022}
}

Comments

A correction is made to a citation. The main result also applies to $L^1([0,1])$

On uniform and coarse rigidity of $L^p([0,1])$

Abstract

Keywords

Cite

Comments

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