Displaying similar documents to “Weak compactness in Banach spaces”

Some properties of weak Banach-Saks operators

Othman Aboutafail, Larbi Zraoula, Noufissa Hafidi (2021)

Mathematica Bohemica

Similarity:

We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).

Weak compactness and σ-Asplund generated Banach spaces

M. Fabian, V. Montesinos, V. Zizler (2007)

Studia Mathematica

Similarity:

σ-Asplund generated Banach spaces are used to give new characterizations of subspaces of weakly compactly generated spaces and to prove some results on Radon-Nikodým compacta. We show, typically, that in the framework of weakly Lindelöf determined Banach spaces, subspaces of weakly compactly generated spaces are the same as σ-Asplund generated spaces. For this purpose, we study relationships between quantitative versions of Asplund property, dentability, differentiability, and of weak...