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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
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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
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
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
We are concerned in this paper with the density of functionals which do not attain their norms in Banach spaces. Some earlier results given for separable spaces are extended to the nonseparable case. We obtain that a Banach space X is reflexive [...]texto impreso
Let M be the collection of all intersections of balls, considered as a subset of the hyperspace H of all closed, convex and bounded sets of a Banach space, furnished with the Hausdorff metric. We prove that M is uniformly very porous if and only[...]texto impreso
We give several results dealing with denseness of certain classes of norms with many vertex points. We prove that, in Banach spaces with the Mazur or the weak* Mazur intersection property, every ball (convex body) can be uniformly approximated b[...]texto impreso
Jiménez Sevilla, María del Mar ; Granero, A. S. ; Moreno, José Pedro | Cambridge Univ Press | 2002-06We prove that spaces with an uncountable omega-independent family fail the Kunen-Shelah property. Actually, if {x(i)}(iis an element ofI) is an uncountable w-independent family, there exists an uncountable subset J.C I such that x(j) is not an e[...]texto impreso
Let ? be a regular cardinal. It is proved, among other things, that: (i) if J(?) is the corresponding long James space, then every closed subspace Y ? J(?), with Dens (Y) = ?, has a copy of 2(?) complemented in J(?); (ii) if Y is a closed subspa[...]texto impreso
In this paper we give new sufficient and necessary conditions for a Banach space to be equivalently renormed with the Mazur intersection property. As a consequence, several examples and applications of these results are obtained. Among them, it [...]texto impreso
Consider the isometric property (P): the restriction to the unit ball of every bounded linear functional is sequentially continuous in the ball topology. We present in this paper a systematic study of this property, which is a sequential version[...]texto impreso
We answer a question posed by J. R. Giles, D. A. Gregory and B. Sims, on the Mazur intersection property, by exhibiting a class of non Asplund spaces admitting an equivalent norm with the above property. On the other hand, if the continuum hypot[...]
