The Banach-Saks property in rearrangement invariant spaces
P. G. Dodds, E. M. Semenov, F. A. Sukochev (2004)
Studia Mathematica
Similarity:
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...