Compactness in Lipschitz spaces and around. (English) Zbl 1534.46015
Authors’ abstract: The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/Hölder continuous mappings from an arbitrary (not necessarily compact) metric space to a normed space. To this end some extensions and generalizations of existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces are established. Those auxiliary results, which are interesting in their own right since they use a new concept of equicontinuity, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.
Reviewer: José Mendoza (Madrid)
MSC:
| 46B50 | Compactness in Banach (or normed) spaces |
| 26A16 | Lipschitz (Hölder) classes |
| 46E15 | Banach spaces of continuous, differentiable or analytic functions |
Keywords:
compactness criterion; equinormed set; precompactness; relative compactness; space of continuous mappings; space of bounded mappings; space of Hölder continuous mappings; space of Lipschitz continuous mappingsReferences:
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