On the structure of Lipschitz-free spaces
By Marek Cúth, M. Doucha, Przemyslaw Wojtaszczyk. 2015
85 citations recorded by the source corpus.
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 $\ell_1$. This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space $K$ such that $F(K)$ is not isomorphic to a subspace of $L_1$ and we show that whenever $M$ is a subset of $R^n$, then $F(M)$ is weakly sequentially complete; in particular, $c_0$ does not embed into $F(M)$.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/304a49f515bd8b68152a94752212cda60a6ca967
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A characterisation of the Daugavet property in spaces of Lipschitz functions (2017, background): “where δx(f) := f(x) for every x ∈ M and f ∈ Lip(M) (see [14, 28], or [9] for the most elementary proof of this fact).”
- On strongly norm attaining Lipschitz maps (2018, background): “It follows since every infinite-dimensional Lipschitz-free space contains an isomorphic copy of `1 (this is folklore, but see [11] where more is proved).”