Banach Spaces with the 4.3. Intersection Property

1980 ◽  
Vol 80 (3) ◽  
pp. 431 ◽  
Author(s):  
Asvald Lima
Keyword(s):  
Banach Spaces ◽  
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 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 Renorming Banach Spaces with the Mazur Intersection Property

1997 ◽  
Vol 144 (2) ◽  
pp. 486-504 ◽  
Author(s):  
M.Jiménez Sevilla ◽  
J.P Moreno
Keyword(s):  
Banach Spaces ◽  
Intersection Property

scholarly journals On denseness of certain norms in Banach spaces

1996 ◽  
Vol 54 (2) ◽  
pp. 183-196 ◽  
Author(s):  
M. Jiménez Sevilla ◽  
J.P. Moreno
Keyword(s):  
Convex Body ◽  
Convex Hull ◽  
Banach Spaces ◽  
Convex Bodies ◽  
Intersection Property ◽  
Closed Convex Hull ◽  
Locally Linear

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 by balls (convex bodies) being the closed convex hull of their strongly vertex points. We also prove that given a countable set F, every norm can be uniformly approximated by norms which are locally linear at each point of F.

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