Mazur's intersection property for finite dimensional sets

1989 ◽  
Vol 283 (1) ◽  
pp. 165-170 ◽  
Author(s):  
Abderrazzak Sersouri
Keyword(s):  
Intersection Property ◽  
Finite Dimensional ◽  
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 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 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.

Uniform Mazur's Intersection Property of Balls

1987 ◽  
Vol 30 (4) ◽  
pp. 455-460 ◽  
Author(s):  
J. H. M. Whitfield ◽  
V. Zizler
Keyword(s):  
Banach Space ◽  
Convex Set ◽  
Closed Ball ◽  
Intersection Property ◽  
Mazur's Intersection Property ◽  
Closed Convex Set

AbstractWe give a dual characterization of the following uniformization of the Mazur's intersection property of balls in a Banach space X: for every ∊ > 0 there is a K > 0 such that whenever a closed convex set C ⊂ X and a point p ∊ X are such that diam C ≤ 1/∊ and dist(p, C) ≤ ∊, then there is a closed ball B of radius ≤ K with B ⊃ C and dist(p,B) ≥ ∊/2.

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