The Banach-Saks property in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, and F. A. Sukochev. "The Banach-Saks property in rearrangement invariant spaces." Studia Mathematica 162.3 (2004): 263-294. <http://eudml.org/doc/284626>.

@article{P2004,
abstract = {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.},
author = {P. G. Dodds, E. M. Semenov, F. A. Sukochev},
journal = {Studia Mathematica},
keywords = {Banach–Saks property; Fatou property; Orlicz space; Lorentz space},
language = {eng},
number = {3},
pages = {263-294},
title = {The Banach-Saks property in rearrangement invariant spaces},
url = {http://eudml.org/doc/284626},
volume = {162},
year = {2004},
}

TY - JOUR
AU - P. G. Dodds
AU - E. M. Semenov
AU - F. A. Sukochev
TI - The Banach-Saks property in rearrangement invariant spaces
JO - Studia Mathematica
PY - 2004
VL - 162
IS - 3
SP - 263
EP - 294
AB - 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.
LA - eng
KW - Banach–Saks property; Fatou property; Orlicz space; Lorentz space
UR - http://eudml.org/doc/284626
ER -