# Characterizations of spreading models of ${l}^{1}$

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 1, page 79-95
- ISSN: 0010-2628

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topKiriakouli, Persephone. "Characterizations of spreading models of $l^1$." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 79-95. <http://eudml.org/doc/248583>.

@article{Kiriakouli2000,

abstract = {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 $l^\{1\}$.},

author = {Kiriakouli, Persephone},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {uniformly bounded sequences of continuous real-valued functions; convergence index; spreading models of $l^\{1\}$; Baire-1 functions; spreading model; pointwise convergent subsequence; unit vector basis of ; generalized Schreier family; convergence index},

language = {eng},

number = {1},

pages = {79-95},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Characterizations of spreading models of $l^1$},

url = {http://eudml.org/doc/248583},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Kiriakouli, Persephone

TI - Characterizations of spreading models of $l^1$

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 1

SP - 79

EP - 95

AB - 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 $l^{1}$.

LA - eng

KW - uniformly bounded sequences of continuous real-valued functions; convergence index; spreading models of $l^{1}$; Baire-1 functions; spreading model; pointwise convergent subsequence; unit vector basis of ; generalized Schreier family; convergence index

UR - http://eudml.org/doc/248583

ER -

## References

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