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Borwein, Jonathan M. ; Jiménez Sevilla, María del Mar ; Moreno, José Pedro | Academic Press-Elsevier Science | 2002-01We prove that every Banach space containing a complemented copy of c0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral spac[...]texto impreso
We characterize the class of separable Banach spaces X such that for every continuous function f : X -> Rand for every continuous function epsilon : X -> (0, +infinity) there exists a C-1 smooth function g: X -> R for which vertical bar f(x) [...]texto impreso
Jaramillo Aguado, Jesús Ángel ; Jiménez Sevilla, María del Mar ; Sánchez González, L. | American Mathematical Society | 2014-03In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative [...]texto impreso
Jaramillo Aguado, Jesús Ángel ; Jiménez Sevilla, María del Mar ; Rodenas Pedregosa, J.L. ; Sánchez González, L. | Pergamon-Elsevier | 2015The concept of subdifferentiability is studied in the context of C-1 Finsler manifolds (modeled on a Banach space with a Lipschitz C-1 bump function). A class of Hamilton-Jacobi equations defined on C-1 Finsler manifolds is studied and several r[...]texto impreso
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It was proved recently that a Banach space fails the Mazur intersection property if and only if the family of all closed, convex and bounded subsets which are intersections of balls is uniformly very porous. This paper deals with the geometrical[...]texto impreso
Granero, A. S. ; Jiménez Sevilla, María del Mar ; Moreno, José Pedro | Polish Acad Sciencies Inst Mathematics | 1998Let BX be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdor metric. In the rst part of this work we study the density character of BX and investigate its connections with the geometry of the space, i[...]texto impreso
Azagra Rueda, Daniel ; Fabián, M. ; Jiménez Sevilla, María del Mar | University of Toronto Press | 2005We establish sufficient conditions on the shape of a set A included in the space Ln s (X; Y ) of the n-linear symmetric mappings between Banach spaces X and Y , to ensure the existence of a Cn-smooth mapping f : X ¡! Y , with bounded support, an[...]texto impreso
We consider the generalized evolution of compact level sets by functions of their normal vectors and second fundamental forms on a Riemannian manifold M. The level sets of a function u;M -> R evolve in such a way whenever u solves an equation u[...]texto impreso
Azagra Rueda, Daniel ; Jiménez Sevilla, María del Mar | Universidad de Extremadura, Departamento de Matemáticas | 2002While the topological and geometrical properties of convex bodies in Banach spaces are quite well understood (including their topological and smooth classification), much less is known about the structure of starlike bodies. Starlike bodies are [...]texto impreso
Granero, A. S. ; Jiménez Sevilla, María del Mar ; Moreno, José Pedro | Hebrew University Magnes Press | 1999-12We prove that every Banach space can be isometrically and 1-complementably embedded into a Banach space which satisfies property ? and has the same character of density. Then we show that, nevertheless, property ? satisfies a hereditary property[...]texto impreso
Granero, A. S. ; Jiménez Sevilla, María del Mar ; Moreno, José Pedro | Universidad de Extremadura, Departamento de Matemáticas | 2004In section 1 we present definitions and basic results concerning the Mazur intersection property (MIP) and some of its related properties as the MIP* . Section 2 is devoted to renorming Banach spaces with MIP and MIP*. Section 3 deals with the c[...]texto impreso
In this note we construct a C?-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.texto impreso
Georgiev, P. G. ; Granero, A. S. ; Jiménez Sevilla, María del Mar ; Moreno, José Pedro | London Mathematical Sociey | 2000-04It is proved that the dual of a Banach space with the Mazur intersection property is almost weak* Asplund. Analogously, the predual of a dual space with the weak* Mazur intersection property is almost Asplund. Through the use of these arguments,[...]texto impreso
Jiménez Sevilla, María del Mar ; Payá Albert, Rafael | Polish Acad Sciencies Inst Mathematics | 1998For each natural number N, we give an example of a Banach space X such that the set of norm attaining N{linear forms is dense in the space of all continuous N{linear forms on X, but there are continuous (N +1){linear forms on X which cannot be a[...]
