Universidad Complutense de Madrid
E-Prints Complutense

On the Kunen-Shelah properties in Banach spaces

Impacto

Downloads

Downloads per month over past year



Granero, A. S. and Jiménez Sevilla, María del Mar and Montesinos, Alejandro and Moreno, José Pedro and Plichko, Anatolij (2003) On the Kunen-Shelah properties in Banach spaces. Studia Mathematica, 157 (2). pp. 97-120. ISSN 0039-3223

[img] PDF
Restringido a Repository staff only

313kB

Official URL: http://journals.impan.gov.pl/sm/index.html


URLURL Type
http://www.impan.pl/Publisher


Abstract

We introduce and study the Kunen-Shelah properties KSi, i = 0, 1,..., 7. Let us highlight for a Banach space X some of our results: (1) X ∗ has a w ∗-nonseparable equivalent dual ball iff X has an ω1-polyhedron (i.e., a bounded family {xi}i<ω1 such that xj / ∈ co({xi: i ∈ ω1 \ {j}}) for every j ∈ ω1) iff X has an uncountable bounded almost biorthonal system (UBABS) of type η, for some η ∈ [0, 1), (i.e., a bounded family {(xα, fα)}1≤α<ω1 ⊂ X × X ∗ such that fα(xα) = 1 and |fα(xβ) | ≤ η, if α = β); (2) if X has an uncountable ω-independent system then X has an UBABS of type η for every η ∈ (0, 1); (3) if X has not the property (C) of Corson, then X has an ω1-polyhedron; (4) X has not an ω1-polyhedron iff X has not a convex right-separated ω1-family (i.e., a bounded family {xi}i<ω1 such that xj / ∈ co({xi: j < i < ω1}) for every j ∈ ω1) iff every w ∗-closed convex subset of X ∗ is w ∗-separable iff every convex subset of X ∗ is w ∗-separable iff µ(X) = 1, µ(X) being the Finet-Godefroy index of X (see [1]).


Item Type:Article
Uncontrolled Keywords:Uncountable basic sequences, Biorthogonal and Markuschevich systems, W-independence, Kunen-Shelah properties.
Subjects:Sciences > Mathematics > Topology
ID Code:22119
Deposited On:26 Jun 2013 17:59
Last Modified:25 Jun 2018 07:05

Origin of downloads

Repository Staff Only: item control page