• DOI:10.4064/SM159-1-6
• Corpus ID: 121923916

Lipschitz-free Banach spaces

@article{Godefroy2003LipschitzfreeBS,
  title={Lipschitz-free Banach spaces},
  author={Gilles Godefroy and Nigel J. Kalton},
  journal={Studia Mathematica},
  year={2003},
  volume={159},
  pages={121-141}
}

• G. Godefroy, N. Kalton
• Published 2003
• Mathematics
• Studia Mathematica

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. 1. Introduction. A (real) Banach space X is in particular a metric space, equipped with the distinguished point f0g, and to such a pointed metric space we can associate the space Lip 0 (X) of all real-valued Lipschitz functions which vanish at 0. We refer to (29) for basic facts on this space and some of its uses. It is clear that Lip 0 (X) is a Banach space when it is equipped with the Lipschitz norm, dened