论文标题
$ \ ell_1 $运输成本空间的等距副本的辅助性
Complementability of isometric copies of $\ell_1$ in transportation cost spaces
论文作者
论文摘要
这项工作旨在建立与运输成本空间结构有关的新结果。由于这些空间在各种情况下进行了研究和应用，因此它们也以不同的名称（例如Arens-Eells空间，无Lipschitz的空间和Wasserstein Spaces）而闻名。本文的主要结果指出，如果公制空间$ x $是这样的，则$ x $的运输成本空间包含$ \ ell_1 $的等轴测副本，则它包含$ 1 $ - 完整的等轴测副本的$ \ ell_1 $。
This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space $X$ is such that the transportation cost space on $X$ contains an isometric copy of $\ell_1$, then it contains a $1$-complemented isometric copy of $\ell_1$.
