Lipschitz-free Banach spaces

G. Godefroy; N. J. Kalton

Studia Mathematica (2003)

  • Volume: 159, Issue: 1, page 121-141
  • ISSN: 0039-3223

Abstract

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

How to cite

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G. Godefroy, and N. J. Kalton. "Lipschitz-free Banach spaces." Studia Mathematica 159.1 (2003): 121-141. <http://eudml.org/doc/285365>.

@article{G2003,
abstract = {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.},
author = {G. Godefroy, N. J. Kalton},
journal = {Studia Mathematica},
keywords = {Lipschitz isomorphism; bounded approximation property; weakly compactly generated space; Lipschitz free space},
language = {eng},
number = {1},
pages = {121-141},
title = {Lipschitz-free Banach spaces},
url = {http://eudml.org/doc/285365},
volume = {159},
year = {2003},
}

TY - JOUR
AU - G. Godefroy
AU - N. J. Kalton
TI - Lipschitz-free Banach spaces
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 1
SP - 121
EP - 141
AB - 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.
LA - eng
KW - Lipschitz isomorphism; bounded approximation property; weakly compactly generated space; Lipschitz free space
UR - http://eudml.org/doc/285365
ER -

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