Affine approximation of Lipschitz functions and nonlinear quotients

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.

authors

• Johnson, William

published proceedings

• GEOMETRIC AND FUNCTIONAL ANALYSIS

altmetric score

• 5.016

author list (cited authors)

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

citation count

• 38

complete list of authors

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

publication date

• January 1999

publisher

• Springer Nature  Publisher

published in

• GEOMETRIC AND FUNCTIONAL ANALYSIS  Journal

Digital Object Identifier (DOI)

• 10.1007/s000390050108

start page

• 1092

end page

• 1127

volume

• 9

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs000390050108