Compactness in Lipschitz spaces and around
Functional Analysis
2023-06-21 v3
Abstract
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces needed to be established. Those auxiliary results, which are interesting on their own since they use a concept of equicontinuity not seen in the literature, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.
Cite
@article{arxiv.2205.04543,
title = {Compactness in Lipschitz spaces and around},
author = {Jacek Gulgowski and Piotr Kasprzak and Piotr Maćkowiak},
journal= {arXiv preprint arXiv:2205.04543},
year = {2023}
}
Comments
This version has been accepted for publication in Studia Mathematica