Non-Commutative Banach Function Spaces.
The Banach-Saks property in rearrangement invariant spaces
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...
RUC systems in rearrangement invariant spaces
We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.
Banach-Saks properties in symmetric spaces of measurable operators
We study Banach-Saks properties in symmetric spaces of measurable operators. A principal result shows that if the symmetric Banach function space E on the positive semiaxis with the Fatou property has the Banach-Saks property then so also does the non-commutative space E(ℳ,τ) of τ-measurable operators affiliated with a given semifinite von Neumann algebra (ℳ,τ).
Page 1