Weak⁎-sequential properties of Johnson–Lindenstrauss spaces

A Banach space X is said to have Efremov's property (E) if every element of the weak⁎-closure of a convex bounded set C⊆X⁎ is the weak⁎-limit of a sequence in C. By assuming the Continuum Hypothesis, we prove that there exist maximal almost disjoint families of infinite subsets of N for which t...

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Bibliographic Details
Published in:Journal of functional analysis 2019-05, Vol.276 (10), p.3051-3066
Main Authors: Avilés, Antonio, Martínez-Cervantes, Gonzalo, Rodríguez, José
Format: Article
Language:English
Subjects:
Almost disjoint family
Johnson–Lindenstrauss space
Weak⁎-sequential closure
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Summary:A Banach space X is said to have Efremov's property (E) if every element of the weak⁎-closure of a convex bounded set C⊆X⁎ is the weak⁎-limit of a sequence in C. By assuming the Continuum Hypothesis, we prove that there exist maximal almost disjoint families of infinite subsets of N for which the corresponding Johnson–Lindenstrauss spaces enjoy (resp. fail) property (E). This is related to a gap in Plichko (2015) [12] and allows to answer (consistently) questions of Plichko and Yost.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2018.09.007