论文标题
在等距嵌入到强大规范的Lipschitz函数中
On isometric embeddings into the set of strongly norm-attaining Lipschitz functions
论文作者
论文摘要
在本文中，我们提供了一个无限的度量空间$ m $，以使强烈标准的Lipschitz函数的集合$ \ mbox {sna}（m）$不包含均值为$ c_0 $的子空间。这回答了AntonioAvilés，GonzaloMartínezCervantes，Abraham Rueda Zoca和Pedro Tradacete提出的一个问题。另一方面，我们证明$ \ mbox {sna}（m）$都包含$ c_0 $的等距副本，每当$ m $是一个不均匀离散的公制空间。特别是，后者适用于无限紧凑的度量空间，而不是适当的度量空间。还给出了在不可分割的环境中的一些积极结果。
In this paper, we provide an infinite metric space $M$ such that the set $\mbox{SNA}(M)$ of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometric to $c_0$. This answers a question posed by Antonio Avilés, Gonzalo Martínez Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. On the other hand, we prove that $\mbox{SNA}(M)$ contains an isometric copy of $c_0$ whenever $M$ is a metric space which is not uniformly discrete. In particular, the latter holds true for infinite compact metric spaces while it does not for proper metric spaces. Some positive results in the non-separable setting are also given.
