Nonlinear quotients

1997/11/10 by Sean M. Bates, William B. Johnson, Bates, Sean M. +7
Mathematics · #46B20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20

paper · pdf · doi:10.48550/arxiv.math/9711206

arxiv created 1998/04/16 · arxiv updated 2009/11/30

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 L_p, 1<p<∞, is already isomorphic to a linear quotient of L_p.

Related

• Property (β) and uniform quotient maps
• The approximation property and Lipschitz mappings on Banach spaces
• Approximation by Lipschitz, analytic maps on certain Banach spaces
• Approximation property in terms of Lipschitz maps via tensor product approach
• Lipschitz Extensions and Approximations