Lipschitz-free Banach spaces

By Gilles Godefroy, Nigel J. Kalton. 2003

329 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/30f3f513631c0a452894dd230fd4df2755c6cecd

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In Algebra and Number Theory

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

On the structure of Lipschitz-free spaces (2015, unknown): “[8, 10, 12, 14, 15, 18, 20].”
On strongly norm attaining Lipschitz maps (2018, background): “= f(x) for x2Mand f2Lip 0 (M;R). We denote by F(M) the norm-closed linear span of (M) in the dual space Lip 0 (M;R) , which is usually called the Lipschitz-free space over M, see the papers [24] and [27], and the book [41] (where it receives the name of Arens-Eells space) for background on this. It ”
Products of Lipschitz-free spaces and applications (2014, background): “nuous isometric isomorphism, thus the choice of dierent base points yields isometrically isomorphic Lipschitz-free spaces. We refer to [14] for a study on Lipschitz functions spaces, and to [14] and [6] for an introduction to Lipschitz-free spaces and its basic properties. One of the main properties”
Tree metrics and their Lipschitz-free spaces (2009, unknown): “31 78 v1 [ m at h. FA ] 2 1 A pr 2 00 9”
ISOMETRIC EMBEDDINGS OF COMPACT SPACES INTO BANACH SPACES (2008, methodology): “In our first lemma, we rephrase Theorem 3.1 of [4] for our particular purpose.”
Lipschitz-type functions on metric spaces (2008, background): “The space B(X) is said to be the Arens–Eells space associated to X in [21], and it is also called the free Banach space over X in [12].”
Free Spaces Over Some Proper Metric Spaces (2014, methodology): “Godefroy and Kalton [6] proved that a Banach space has the λ-BAP if and only if its Lipschitz-free space has the λ-BAP.”
THE DAUGAVET PROPERTY FOR SPACES OF LIPSCHITZ FUNCTIONS (2005, background): “The space Lip(K) has a canonical predual, called the Arens-Eells space in [13] and the Lipschitz free space in [4] and [7].”
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).”
Lipschitz operator ideals and the approximation property (2016, background): “Although in recent years there is an increasing interest for finding results on approximation properties related to Lipschitz functions and the free spaces Æ(X) of metric spaces X (see [15, 16, 21, 22, 29]), there are no explicit definitions of approximation properties on metric spaces.”
On stability of nonlinear non-surjective ε-isometries of Banach spaces (2013, background): “Godefroy and Kalton [9] show some deep relationship between isometry and linear isometry.”