Transitivity of intersection properties of balls.
Rafael Payá Albert (1986)
Extracta Mathematicae
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Rafael Payá Albert (1986)
Extracta Mathematicae
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Tomasz Kania, Tomasz Kochanek (2016)
Studia Mathematica
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Let X be a Banach space. We study the circumstances under which there exists an uncountable set 𝓐 ⊂ X of unit vectors such that ||x-y|| > 1 for any distinct x,y ∈ 𝓐. We prove that such a set exists if X is quasi-reflexive and non-separable; if X is additionally super-reflexive then one can have ||x-y|| ≥ slant 1 + ε for some ε > 0 that depends only on X. If K is a non-metrisable compact, Hausdorff space, then the unit sphere of X = C(K) also contains such a subset; if moreover...
Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)
Colloquium Mathematicae
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We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...
Ehrhard Behrends, Vladimir M. Kadets (2001)
Studia Mathematica
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A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete...
Robert A. McGuigan, Jr. (1970)
Compositio Mathematica
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Cardwell, Antonia E. (2006)
International Journal of Mathematics and Mathematical Sciences
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Maria D. Acosta, Vicente Montesinos (2006)
Acta Universitatis Carolinae. Mathematica et Physica
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Michael Barr (1976)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Félix Cabello Sánchez, Jesús M. Fernández Castillo (1995)
Extracta Mathematicae
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Tanmoy Paul (2012)
Studia Mathematica
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We investigate almost ball remotal and ball remotal subspaces of Banach spaces. Several subspaces of the classical Banach spaces are identified having these properties. Some stability results for these properties are also proved.
Jakub Duda (2007)
Colloquium Mathematicae
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By using D. Preiss' approach to a construction from a paper by J. Matoušek and E. Matoušková, and some results of E. Matoušková, we prove that we can decompose a separable Banach space with modulus of convexity of power type p as a union of a ball small set (in a rather strong symmetric sense) and a set which is Aronszajn null. This improves an earlier unpublished result of E. Matoušková. As a corollary, in each separable Banach space with modulus of convexity of power type p, there...
Anatolij M. Plichko, David Yost (2000)
Extracta Mathematicae
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.