Affine Approximation of Lipschitz Functions and Nonlinear Quotients
نویسندگان
چکیده
New concepts related to approximating a Lipschitz function between Banach spaces by a ne 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 approx imated 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 p is already isomorphic to a linear quotient of Lp
منابع مشابه
[ m at h . FA ] 1 6 A pr 1 99 8 AFFINE APPROXIMATION OF LIPSCHITZ FUNCTIONS AND NONLINEAR QUOTIENTS
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 ...
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Lipschitz quotient mappings and uniform quotient mappings between Banach spaces are introduced and investigated. In particular, it is shown that if a Banach space is a uniform quotient of L p , 1 < p < ∞, then it is isomorphic to a linear quotient of L p. For the purpose of studying quotient mappings and also for their own interest, new concepts related to approximating general Lipschitz functi...
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