Displaying similar documents to “A Note on Differentiability of Lipschitz Maps”

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.

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.

Lipschitz-free Banach spaces

G. Godefroy, N. J. Kalton (2003)

Studia Mathematica

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We show that when a linear quotient map to a separable Banach space X has a Lipschitz right inverse, then it has a linear right inverse. If a separable space X embeds isometrically into a Banach space Y, then Y contains an isometric linear copy of X. This is false for every nonseparable weakly compactly generated Banach space X. Canonical examples of nonseparable Banach spaces which are Lipschitz isomorphic but not linearly isomorphic are constructed. If a Banach space X has the bounded...

Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions

Luděk Zajíček (2014)

Commentationes Mathematicae Universitatis Carolinae

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We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on Γ -almost everywhere Fréchet differentiability of Lipschitz functions on c 0 (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at Γ -almost every x at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are Γ -almost everywhere Fréchet...

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.