# Weak Cauchy sequences in ${L}_{\infty}(\mu ,X)$

Studia Mathematica (1995)

- Volume: 116, Issue: 3, page 271-281
- ISSN: 0039-3223

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topSchlüchtermann, Georg. "Weak Cauchy sequences in $L_{∞}(μ,X)$." Studia Mathematica 116.3 (1995): 271-281. <http://eudml.org/doc/216233>.

@article{Schlüchtermann1995,

abstract = {For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in $L_\{∞\}(μ,X)$, the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of $L_\{∞\}(μ,X)$ is discussed.},

author = {Schlüchtermann, Georg},

journal = {Studia Mathematica},

keywords = {essentially bounded vector-valued functions; measure space; weak Cauchy sequences; distinction between Asplund and conditionally weakly compact subsets},

language = {eng},

number = {3},

pages = {271-281},

title = {Weak Cauchy sequences in $L_\{∞\}(μ,X)$},

url = {http://eudml.org/doc/216233},

volume = {116},

year = {1995},

}

TY - JOUR

AU - Schlüchtermann, Georg

TI - Weak Cauchy sequences in $L_{∞}(μ,X)$

JO - Studia Mathematica

PY - 1995

VL - 116

IS - 3

SP - 271

EP - 281

AB - For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in $L_{∞}(μ,X)$, the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of $L_{∞}(μ,X)$ is discussed.

LA - eng

KW - essentially bounded vector-valued functions; measure space; weak Cauchy sequences; distinction between Asplund and conditionally weakly compact subsets

UR - http://eudml.org/doc/216233

ER -

## References

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- [RU] L. H. Riddle and J. J. Uhl, Martingales and the fine line between Asplund spaces and spaces not containing a copy of ${\ell}_{1}$, in: Martingale Theory in Harmonic Analysis and Banach Spaces, Lecture Notes in Math. 939, Springer, 1983, 145-156.
- [S1] G. Schlüchtermann, Renorming in the space of Bochner integrable functions ${L}_{1}(\mu ,X)$, Manuscripta Math. 73 (1991), 397-409.
- [S2] G. Schlüchtermann, On weakly compact operators, Math. Ann. 292 (1992), 263-266. Zbl0735.47012
- [S3] G. Schlüchtermann, Weak compactness in ${L}_{\infty}(\mu ,X)$, J. Funct. Anal. 125, (1994), 379-388. Zbl0828.46036
- [Ta] M. Talagrand, Weak Cauchy sequences in ${L}^{1}\left(E\right)$, Amer. J. Math. 106 (1984), 703-724. Zbl0579.46025

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