RT Journal Article
T1 On ω-independence and the Kunen-Shelah property
A1 Jiménez Sevilla, María del Mar
A1 Granero, A. S.
A1 Moreno, José Pedro
AB 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.
PB Cambridge Univ Press
SN 0013-0915
YR 2002
FD 2002-06
LK https://hdl.handle.net/20.500.14352/57522
UL https://hdl.handle.net/20.500.14352/57522
LA eng
NO 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.
NO Supported in part by DGICYT grants PB 97-0240 and BMF2000-0609.
NO DGICYT
NO BMF
DS Docta Complutense
RD 4 may 2024