Lipschitz-free Banach spaces

• Autorzy: G. Godefroy , N. J. Kalton
• Języki publikacji: EN

Abstrakty

EN

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 approximation property and Y is Lipschitz isomorphic to X, then Y has the bounded approximation property.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B26: Nonseparable Banach spaces
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 1
• Strony: 121-141

Daty

wydano

2003

Twórcy

autor

G. Godefroy

• Équipe d'Analyse, Université Paris VI, Boîte 186, 4, Place Jussieu, 75252 Paris Cedex 05, France

autor

N. J. Kalton

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/sm159-1-6