论文标题
lipschitz的近似属性在组上不含Lipschitz
Approximation properties in Lipschitz-free spaces over groups
论文作者
论文摘要
我们在紧凑和均匀离散的公制空间上研究无LIPSCHITZ的空间，享有某些高规律性的特性 - 具有左右公制的组结构。使用谐波分析方法，我们表明，鉴于配备有任意兼容的剩余左右公制$ d $的紧凑型Metrizable $ g $，$ g $，$ \ mathcal {f}（g，d）$的无Lipschitz-friage空间满足了度量近似属性。我们还表明，鉴于一个有限生成的$ g $，其单词$ d $，从一类承认某种特殊类型的梳子的组中，其中包括所有双曲线组和大型的ARTIN组，$ \ MATHCAL {f}（g，d）$具有Schauder的基础。讨论了示例和应用。特别是，对于任何净$ n $，在真正的双曲线$ n $ -space $ \ mathbb {h}^n $，$ \ mathcal {f}（n）的基础上。
We study Lipschitz-free spaces over compact and uniformly discrete metric spaces enjoying certain high regularity properties - having group structure with left-invariant metric. Using methods of harmonic analysis we show that, given a compact metrizable group $G$ equipped with an arbitrary compatible left-invariant metric $d$, the Lipschitz-free space over $G$, $\mathcal{F}(G,d)$, satisfies the metric approximation property. We show also that, given a finitely generated group $G$, with its word metric $d$, from a class of groups admitting a certain special type of combing, which includes all hyperbolic groups and Artin groups of large type, $\mathcal{F}(G,d)$ has a Schauder basis. Examples and applications are discussed. In particular, for any net $N$ in a real hyperbolic $n$-space $\mathbb{H}^n$, $\mathcal{F}(N)$ has a Schauder basis.
