Biblioteca de la Universidad Complutense de Madrid

On ω-independence and the Kunen-Shelah property


Jiménez Sevilla, María del Mar y Granero, A. S. y Moreno, José Pedro (2002) On ω-independence and the Kunen-Shelah property. Proceedings of the Edinburgh Mathematical Society, 45 (2). pp. 391-395. ISSN 0013-0915

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.


URL Oficial:


We prove that spaces with an uncountable omega-independent family fail the Kunen-Shelah property. Actually, if {x(i)}(iis an element ofI) is an uncountable w-independent family, there exists an uncountable subset J.C I such that x(j) is not an element of (conv) over bar({x(i)}(iis an element ofj/{j}) for every j is an element of J. This improves a previous result due to Sersouri, namely that every uncountable omega-independent family contains a convex right-separated subfamily.

Tipo de documento:Artículo
Información Adicional:

Supported in part by DGICYT grants PB 97-0240 and BMF2000-0609.

Palabras clave:ω-independence; non-separable Banach spaces; Kunen–Shelah property
Materias:Ciencias > Matemáticas > Topología
Código ID:16386

C. Finet and G. Godefroy, Biorthogonal systems and big quotient spaces, Contemp. Math. 85 (1989), 87–110.

D. H. Fremlin and A. Sersouri, On ω-independence in separable Banach spaces, Q. J. Math. 39 (1988), 323–331.

A. S. Granero, M. Jiménez-Sevilla and J. P. Moreno, Convex sets in Banach spaces and a problem of Rolewicz, Studia Math. 129 (1998), 19–29.

M. Jiménez-Sevilla and J. P. Moreno, Renorming Banach spaces with the Mazur intersection property, J. Funct. Analysis 144 (1997), 486–504.

N. J. Kalton, Independence in separable Banach spaces, Contemp. Math. 85 (1989), 319–323.

S. Negrepontis, Banach spaces and topology, in Handbook of set-theoretic topology, pp. 1045–1142 (North-Holland, Amsterdam, 1984).

R. R. Phelps, Convex functions, monotone operators and differentiability, 2nd edn, Lecture Notes in Mathematics, no. 1364 (Springer, 1993).

A. Sersouri, ω-independence in nonseparable Banach spaces, Contemp. Math. 85 (1989), 509–512.

S. Shelah, A Banach space with few operators, Israel J. Math. 30 (1978), 181–191.

S. Shelah, Uncountable constructions for B.A., e.c. groups and Banach spaces, Israel J. Math. 51 (1985), 273–297.

Depositado:17 Sep 2012 08:47
Última Modificación:10 Feb 2016 16:03

Sólo personal del repositorio: página de control del artículo