The Banach–Saks property in rearrangement invariant spaces
Volume 162 / 2004
Studia Mathematica 162 (2004), 263-294
MSC: Primary 46A30; Secondary 46B20, 46B15.
DOI: 10.4064/sm162-3-6
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.
