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Título:
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Rolle’s Theorem and Negligibility of Points in Infinite Dimensional Banach Spaces
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Autores:
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Azagra Rueda, Daniel ;
Gómez Gil, Javier ;
Jaramillo Aguado, Jesús Ángel
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Tipo de documento:
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texto impreso
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Editorial:
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Elsevier, 1997-09-15
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores
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Tipo = Artículo
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Resumen:
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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).
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En línea:
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https://eprints.ucm.es/id/eprint/14492/1/1997rolle%27sB.pdf
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