Displaying similar documents to “Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces”

Spaces of Lipschitz and Hölder functions and their applications.

Nigel J. Kalton (2004)

Collectanea Mathematica

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We study the structure of Lipschitz and Hölder-type spaces and their preduals on general metric spaces, and give applications to the uniform structure of Banach spaces. In particular we resolve a problem of Weaver who asks wether if M is a compact metric space and 0 < α < 1, it is always true the space of Hölder continuous functions of class α is isomorphic to l. We show that, on the contrary, if M is a compact convex subset of a Hilbert space this isomorphism holds if...

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...