This is an announcement for the paper “Banach spaces with weak*-sequential dual ball” by Gonzalo Martínez-Cervanteshttps://arxiv.org/find/math/1/au:+Martinez_Cervantes_G/0/1/0/all/0/1.
Abstract: A topological space is said to be sequential if every sequentially closed subspace is closed. We consider Banach spaces with weak$^*$-sequential dual ball. In particular, we show that if $X$ is a Banach space with weak$^*$-sequentially compact dual ball and $Y\subset X$ is a subspace such that $Y$ and $X/Y$ have weak$^*$-sequential dual ball, then X has weak$^*$-sequential dual ball. As an application we obtain that the Johnson-Lindenstrauss space $JL_2$ and $C(K)$ for $K$ scattered compact space of countable height are examples of Banach spaces with weak$^*$-sequential dual ball, answering in this way a question of A. Plichko.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1612.05948