Nonlinear quotients
Functional Analysis
2007-05-23 v2
Abstract
New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces , for which any Lipschitz function from to can be so approximated is obtained. This is applied to the study of Lipschitz and uniform quotient mappings between Banach spaces. It is proved, in particular, that any Banach space which is a uniform quotient of , , is already isomorphic to a linear quotient of .
Cite
@article{arxiv.math/9711206,
title = {Nonlinear quotients},
author = {Sean M. Bates and William B. Johnson and Joram Lindenstrauss and D. Preiss and Gideon Schechtman},
journal= {arXiv preprint arXiv:math/9711206},
year = {2007}
}