RT Journal Article
T1 On the Kunen-Shelah properties in Banach spaces
A1 Suárez Granero, Antonio
A1 Jiménez Sevilla, María Del Mar
A1 Montesinos, Alejandro
A1 Moreno, José Pedro
A1 Plichko, Anatolij
AB 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]).
PB Polish Acad Sciencies Inst Mathematics
SN 0039-3223
YR 2003
FD 2003
LK https://hdl.handle.net/20.500.14352/58609
UL https://hdl.handle.net/20.500.14352/58609
LA eng
NO DGICYT
DS Docta Complutense
RD 7 abr 2025