Weak^*-sequential properties of Johnson-Lindenstrauss spaces

2018/04/27 by Avilés, Antonio, Martínez-Cervantes, Gonzalo, Rodríguez, José · 1 citation
#46A50 #46B26 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1804.10350

Abstract

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 [A. Plichko, Three sequential properties of dual Banach spaces in the weak^* topology, Topology Appl. 190 (2015), 93--98] and allows to answer (consistently) questions of Plichko and Yost.

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