Factoring Operators Through Banach Lattices Not Containing C(0, 1).
Factorization and domination of positive Banach-Saks operators
It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.
Factorization by Lattice Homomorphisms.
Finite-dimensional subspaces of uniformly convex and uniformly smooth Banach lattices and trace classes
Fréchet-spaces-valued measures and the AL-property.
Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.