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Rolle’s Theorem and Negligibility of Points in Infinite Dimensional Banach Spaces


Azagra Rueda, Daniel y Gómez Gil, Javier y Jaramillo Aguado, Jesús Ángel (1997) Rolle’s Theorem and Negligibility of Points in Infinite Dimensional Banach Spaces. Journal of Mathematical Analysis and Applications, 213 (2). pp. 487-495. ISSN 0022-247X

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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).

Tipo de documento:Artículo
Palabras clave:Rolle’s theorem in infinite-dimensional Banach spaces; Approximate Rolle’s theorem; Continuous norm whose dual norm is locally uniformly rotund; C1 bump function
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:14492

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Última Modificación:28 Ene 2016 16:01

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