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Displaying similar documents to “On the range of the derivative of a smooth function and applications.”

Smooth approximations without critical points

Petr Hájek, Michal Johanis (2003)

Open Mathematics

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In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains...

A survey on the Szlenk index and some of its applications.

Gilles Lancien (2006)

RACSAM

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We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.

A converse to Amir-Lindenstrauss theorem in complex Banach spaces.

Ondrej F. K. Kalenda (2006)

RACSAM

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We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.

A one-sided version of Alexiewicz-Orlicz's differentiability theorem.

E. Corbacho, A. Plichko, V. Tarieladze (2005)

RACSAM

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Modificando adecuadamente el método de un trabajo olvidado [1], probamos que si una aplicación continua, de un subconjunto abierto no vacío U de un espacio vectorial topológico metrizable separable y de Baire E, en un espacio localmente convexo, es direccionalmente diferenciable por la derecha en U según un subconjunto comagro de E, entonces, es genéricamente Gâteaux diferenciable en U. Nuestro resultado implica que cualquier espacio vectorial topológico, metrizable, separable y de Baire,...