Subspaces of Hilbert-generated Banach spaces and the quantification of super weak compactness |
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Affiliation: | Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain |
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Abstract: | We introduce a measure of super weak noncompactness Γ defined for bounded subsets and bounded linear operators 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, 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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Keywords: | Super weak compactness Uniformly weakly null sets Hilbert-generated spaces Uniformly Eberlein compact sets |
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