2026-06-01T01:22:45Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/586092024-07-15T13:47:06Zcom_20.500.14352_14col_20.500.14352_15

On the Kunen-Shelah properties in Banach spaces Suárez Granero, Antonio Jiménez Sevilla, María Del Mar Montesinos, Alejandro Moreno, José Pedro Plichko, Anatolij 515.1 Uncountable basic sequences Biorthogonal and Markuschevich systems W-independence Kunen-Shelah properties. Topología 1210 Topología 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]). DGICYT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T18:47:07Z 2023-06-20T18:47:07Z 2003 journal article https://hdl.handle.net/20.500.14352/58609 0039-3223 eng PB97-0240 PB97-0377 restricted access application/pdf Polish Acad Sciencies Inst Mathematics