2022/03/01 by Guillaume Grelier, M. Raja, Grelier, Guillaume +1
Mathematics · Computer Science · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2203.00338
We introduce a measure of super weak noncompactness Γ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert generated space. The use of super weak compactness and Γ casts light on the structure of these Banach spaces and complements the work of Argyros, Fabian, Farmaki, Godefroy, Hájek, Montesinos,\linebreak Troyanski and Zizler on this subject. A particular kind of relatively super weakly compact sets, namely uniformly weakly null sets, plays an important role and exhibits connections with Banach-Saks type properties.