Displaying similar documents to “An upper bound for the Lipschitz retraction constant in l₁”

Bi-Lipschitz Bijections of Z

Itai Benjamini, Alexander Shamov (2015)

Analysis and Geometry in Metric Spaces

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It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.

Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Adam Parusiński (2005)

Annales Polonici Mathematici

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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.

A note on Lipschitz isomorphisms in Hilbert spaces

Dean Ives (2010)

Commentationes Mathematicae Universitatis Carolinae

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We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space?

A Note on Differentiability of Lipschitz Maps

Rafał Górak (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.

Lipschitz approximable Banach spaces

Gilles Godefroy (2020)

Commentationes Mathematicae Universitatis Carolinae

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We show the existence of Lipschitz approximable separable spaces which fail Grothendieck's approximation property. This follows from the observation that any separable space with the metric compact approximation property is Lipschitz approximable. Some related results are spelled out.

Products of Lipschitz-free spaces and applications

Pedro Levit Kaufmann (2015)

Studia Mathematica

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We show that, given a Banach space X, the Lipschitz-free space over X, denoted by ℱ(X), is isomorphic to ( ∑ n = 1 ∞ ℱ ( X ) ) ℓ ₁ . Some applications are presented, including a nonlinear version of Pełczyński’s decomposition method for Lipschitz-free spaces and the identification up to isomorphism between ℱ(ℝⁿ) and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into ℝⁿ and which contains a subset that is Lipschitz equivalent to the unit ball of ℝⁿ. We also show...