This is an announcement for the paper “Weak$^*$-sequential properties of Johnson-Lindenstrauss spaces” by Antonio Aviléshttps://arxiv.org/search?searchtype=author&query=Avil%C3%A9s%2C+A, Gonzalo Martínez-Cervanteshttps://arxiv.org/search?searchtype=author&query=Mart%C3%ADnez-Cervantes%2C+G, José Rodríguezhttps://arxiv.org/search?searchtype=author&query=Rodr%C3%ADguez%2C+J.

Abstract: A Banach space $X$ is said to have Efremov's property $(\epsilon)$ if every element of the weak$^*$-closure of a convex bounded set $C\subset X^*$ 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 $\mathbb{N}$ for which the corresponding Johnson-Lindenstrauss spaces enjoy (resp. fail) property $(\epsilon)$. 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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1804.10350