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Title: Characterizations of spreading models of $l^1$ (English)
Author: Kiriakouli, P.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 1
Year: 2000
Pages: 79-95
Category: math
Summary: Rosenthal in [11] proved that if $(f_{k})$ is a uniformly bounded sequence of real-valued functions which has no pointwise converging subsequence then $(f_{k})$ has a subsequence which is equivalent to the unit basis of $l^{1}$ in the supremum norm. Kechris and Louveau in [6] classified the pointwise convergent sequences of continuous real-valued functions, which are defined on a compact metric space, by the aid of a countable ordinal index ``$\gamma $''. In this paper we prove some local analogues of the above Rosenthal 's theorem (spreading models of $l^{1}$) for a uniformly bounded and pointwise convergent sequence $(f_{k})$ of continuous real-valued functions on a compact metric space for which there exists a countable ordinal $\xi$ such that $\gamma ((f_{n_{k}}))> \omega^{\xi}$ for every strictly increasing sequence $(n_{k})$ of natural numbers. Also we obtain a characterization of some subclasses of Baire-1 functions by the aid of spreading models of $l^{1}$. (English)
Keyword: uniformly bounded sequences of continuous real-valued functions
Keyword: convergence index
Keyword: spreading models of $l^{1}$
Keyword: Baire-1 functions
MSC: 46B20
MSC: 46B99
MSC: 46E15
MSC: 46E99
MSC: 54C35
idZBL: Zbl 1039.46010
idMR: MR1756928
Date available: 2009-01-08T18:58:40Z
Last updated: 2012-04-30
Stable URL:
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