On the structure of Banach spaces with Mazur's intersection property

1991 ◽  
Vol 291 (1) ◽  
pp. 463-473 ◽  
Author(s):  
P. S. Kenderov ◽  
J. R. Giles
Keyword(s):  
Banach Spaces ◽  
Intersection Property ◽  
Mazur's Intersection Property

scholarly journals On biorthogonal systems and Maxur's intersection property

2004 ◽  
Vol 69 (1) ◽  
pp. 107-111 ◽  
Author(s):  
Jan Rychtář
Keyword(s):  
Banach Spaces ◽  
Intersection Property ◽  
Sufficient Condition ◽  
Biorthogonal Systems ◽  
Markushevich Basis ◽  
Mazur's Intersection Property

We give a characterisation of Banach spaces X containing a subspace with a shrinking Markushevich basis {xγ, fγ}γ∈Γ. This gives a sufficient condition for X to have a renorming with Mazur's intersection property.

Un Théorème de Transfert Pour la Propriété des Boules

1987 ◽  
Vol 30 (3) ◽  
pp. 295-300 ◽  
Author(s):  
Robert Deville
Keyword(s):  
Banach Spaces ◽  
Equivalent Norm ◽  
Intersection Property ◽  
Mazur's Intersection Property

AbstractWe show that, if X and Y are Banach spaces such that X has the Mazur's intersection property and such that there exists T, an operator from Y into X so that T* and T** are injective, then there exists on Y an equivalent norm which has the Mazur's intersection property.We deduce from this result and from a result of M. Talagrand that there exists on the long James space J(η) an equivalent norm which has the Mazur's intersection property.

scholarly journals Mazur's intersection property of balls for compact convex sets

1987 ◽  
Vol 35 (2) ◽  
pp. 267-274 ◽  
Author(s):  
J. H. M. Whitfield ◽  
V. Zizler
Keyword(s):  
Banach Space ◽  
Uniform Convergence ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Intersection Property ◽  
Compact Sets ◽  
Compact Convex Set ◽  
Mazur's Intersection Property

We show that every compact convex set in a Banach space X is an intersection of balls provided the cone generated by the set of all extreme points of the dual unit ball of X* is dense in X* in the topology of uniform convergence on compact sets in X. This allows us to renorm every Banach space with transfinite Schauder basis by a norm which shares the mentioned intersection property.

scholarly journals Balls intersection properties of Banach spaces

1992 ◽  
Vol 45 (2) ◽  
pp. 333-342 ◽  
Author(s):  
Dongjian Chen ◽  
Zhibao Hu ◽  
Bor-Luh Lin
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Intersection Property ◽  
Necessary And Sufficient Conditions ◽  
Asplund Space ◽  
Necessary And Sufficient

Necessary and sufficient conditions for a Banach space with the Mazur intersection property to be an Asplund space are given. It is proved that Mazur intersection property is determined by the separable subspaces of the space. Corresponding problems for a space to have the ball-generated property are considered. Some comments on possible renorming so that a space having the Mazur intersection property are given.

scholarly journals Characterisation of normed linear spaces with Mazur's intersection property

1978 ◽  
Vol 18 (1) ◽  
pp. 105-123 ◽  
Author(s):  
J.R. Giles ◽  
D.A. Gregory ◽  
Brailey Sims
Keyword(s):  
Euclidean Space ◽  
Convex Set ◽  
Intersection Property ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Strongly Exposed Points ◽  
Denting Points ◽  
Mazur's Intersection Property ◽  
Closed Convex Set ◽  
Space Property

Normed linear spaces possessing the euclidean space property that every bounded closed convex set is an intersection of closed balls, are characterised as those with dual ball having weak* denting points norm dense in the unit sphere. A characterisation of Banach spaces whose duals have a corresponding intersection property is established. The question of the density of the strongly exposed points of the ball is examined for spaces with such properties.

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