论文标题
$ l_ {p} $没有eprovariant的粗嵌入到$ \ ell_p $中
There is no equivariant coarse embedding of $L_{p}$ into $\ell_p$
论文作者
论文摘要
在本文中，我们证明$ l_ {p} $不承认将equivariant的粗嵌入到$ \ ell_p $中，即没有适当的，仿射的，等距为$ l_ {p} $，该动作是在与标准度量$ ||的添加下相同的。 。 || _p $，on $ \ ell_p $。这是通过将$ l_ {p} $的表示形式显示为$ isom（\ ell_p）$必须是微不足道的，这使我们可以将问题简化为bi-lipschitz设置。
In this paper we prove that $L_{p}$ does not admit an equivariant coarse embedding into $\ell_p$ i.e there is no proper, affine, isometric action of $L_{p}$, viewed as a group under addition with the standard metric $|| . ||_p$, on $\ell_p$. This is done by showing that representations of $L_{p}$ into $ Isom(\ell_p)$ has to be trivial, which allows us to reduce the question to bi-Lipschitz setting.
