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zbMATH Open
Article . 2016
Data sources: zbMATH Open
https://dx.doi.org/10.48550/ar...
Article . 2015
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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On the structure of Lipschitz-free spaces

Authors: Cúth, Marek; Doucha, Michal; Wojtaszczyk, Przemysław;

On the structure of Lipschitz-free spaces

Abstract

In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space over an infinite metric space contains a complemented copy of ℓ 1 \ell _1 . This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space K K such that F ( K ) \mathcal {F}(K) is not isomorphic to a subspace of L 1 L_1 and we show that whenever M M is a subset of R n \mathbb {R}^n , then F ( M ) \mathcal {F}(M) is weakly sequentially complete; in particular, c 0 c_0 does not embed into F ( M ) \mathcal {F}(M) .

Keywords

Mathematics - Functional Analysis, Isomorphic theory (including renorming) of Banach spaces, Metric spaces, metrizability, FOS: Mathematics, Lipschitz free space, embedding into \(L_1\), weakly sequentially complete Banach spaces, 46B03, 54E35, Classical Banach spaces in the general theory, Functional Analysis (math.FA)

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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!
44
Top 10%
Top 10%
Top 10%
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bronze
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