Affine Approximation of Lipschitz Functions and Nonlinear Quotients Academic Article uri icon

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 X, Y for which any Lipschitz function from X to Y 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 Lp, 1 < p < ∞, is already isomorphic to a linear quotient of Lp.

altmetric score

  • 5.016

author list (cited authors)

  • Bates, S., Johnson, W. B., Lindenstrauss, J., Preiss, D., & Schechtman, G.

citation count

  • 35

complete list of authors

  • Bates, S||Johnson, WB||Lindenstrauss, J||Preiss, D||Schechtman, G

publication date

  • December 1999