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Proceedings of the Royal Society of Edinburgh Section A Mathematics
Article . 2021 . Peer-reviewed
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Article . 2021
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RETRACTED - Compact reduction in Lipschitz-free spaces

Retracted: Compact reduction in Lipschitz-free spaces
Authors: Ramón J. Aliaga; Camille Noûs; Colin Petitjean; Antonín Procházka;

RETRACTED - Compact reduction in Lipschitz-free spaces

Abstract

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are: $\mathcal {F}(X)$ is weakly sequentially complete for every superreflexive Banach space $X$ , and $\mathcal {F}(M)$ has the Schur property and the approximation property for every scattered complete metric space $M$ .

Keywords

Lipschitz lifting property, approximation property, Lipschitz function, Lipschitz-free space, Dunford-Pettis property, Complete metric spaces, weak sequential completeness, Classical Banach spaces in the general theory, Schur property

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Top 10%
Average
bronze
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