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 $l^{1}$.
@article{119142,
author = {Persephone Kiriakouli},
title = {Characterizations of spreading models of $l^1$},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {79-95},
zbl = {1039.46010},
mrnumber = {1756928},
language = {en},
url = {http://dml.mathdoc.fr/item/119142}
}
Kiriakouli, Persephone. Characterizations of spreading models of $l^1$. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 79-95. http://gdmltest.u-ga.fr/item/119142/
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