期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 232, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2023.113287
关键词
Strong norm attainment; Space of Lipschitz functions; Linear subspaces; Embedding ofc0
In this paper, an infinite metric space M is introduced where the set of strongly norm-attaining Lipschitz functions on M does not contain a subspace which is linear isometric to c0. This paper answers a question posed by Antonio Aviles, Gonzalo Martinez-Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. It is also proven that the set contains an isometric copy of c0 whenever M is an infinite metric space that is not uniformly discrete.
In this paper, we provide an infinite metric space M such that the set SNA(M) of strongly norm-attaining Lipschitz functions on M does not contain a subspace which is linearly isometric to c0. This answers a question posed by Antonio Aviles, Gonzalo Martinez-Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. On the other hand, we prove that SNA(M) contains an isometric copy of c0 whenever M is an infinite metric space which is not uniformly discrete. In particular, the latter holds true for all infinite compact metric spaces while it does not hold true for all proper metric spaces. We also provide some positive results in the non-separable setting.& COPY; 2023 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据