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arXiv · 2203.00338

Applications of the quantification of super weak compactness

Guillaume Grelier·Matías Raja
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Abstract

We introduce a measure of super weak noncompactness $\Gamma$ 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 $\Gamma$ casts light on the structure of these Banach spaces and complements the work of Argyros, Fabian, Farmaki, Godefroy, H\'ajek, 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.

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Guillaume Grelier, Matías Raja. 2022-03-01. Applications of the quantification of super weak compactness. https://arxiv.org/abs/2203.00338

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