On isometric embeddings into the set of strongly norm-attaining Lipschitz functions

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.

Automated summary

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.