The Banach–Saks property in rearrangement
invariant spaces
Studia Mathematica, Tome 162 (2004) no. 3, pp. 263-294
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
This paper studies the Banach–Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space $E$ with the Fatou property has the Banach–Saks property if and only if $E$ has the Banach–Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach–Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the Banach–Saks property.
Keywords:
paper studies banach saks property rearrangement invariant spaces positive half line principal result paper shows separable rearrangement invariant space fatou property has banach saks property only has banach saks property disjointly supported sequences further orlicz lorentz spaces banach saks property equivalent separability although separable parts marcinkiewicz spaces fail banach saks property
Affiliations des auteurs :
P. G. Dodds 1 ; E. M. Semenov 2 ; F. A. Sukochev 1
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author = {P. G. Dodds and E. M. Semenov and F. A. Sukochev},
title = {The {Banach{\textendash}Saks} property in rearrangement
invariant spaces},
journal = {Studia Mathematica},
pages = {263--294},
publisher = {mathdoc},
volume = {162},
number = {3},
year = {2004},
doi = {10.4064/sm162-3-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm162-3-6/}
}
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P. G. Dodds; E. M. Semenov; F. A. Sukochev. The Banach–Saks property in rearrangement invariant spaces. Studia Mathematica, Tome 162 (2004) no. 3, pp. 263-294. doi: 10.4064/sm162-3-6
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