RT Journal Article
T1 Rolle’s Theorem and Negligibility of Points in Infinite Dimensional Banach Spaces
A1 Azagra Rueda, Daniel
A1 Gómez Gil, Javier
A1 Jaramillo Aguado, Jesús Ángel
AB In this note we prove that if a differentiable function oscillates between y« and « on the boundary of the unit ball then there exists a point in the interior of the ball in which the differential of the function has norm equal or less than« . This kind of approximate Rolle’s theorem is interesting because an exact Rolle’s theorem does not hold in many infinite dimensional Banach spaces. A characterization of those spaces in which Rolle’s theorem does not hold is given within a large class of Banach spaces. This question is closely related to the existence of C1 diffeomorphisms between a Banach space X and X _ _04 which are the identity out of a ball, and we prove that such diffeomorphisms exist for every C1 smooth Banach space which can be linearly injected into a Banach space whose dual norm is locally uniformly rotund (LUR).
PB Elsevier
SN 0022-247X
YR 1997
FD 1997-09-15
LK https://hdl.handle.net/20.500.14352/57128
UL https://hdl.handle.net/20.500.14352/57128
LA eng
DS Docta Complutense
RD 13 abr 2025