Banach spaces with weak*-sequential dual ball
Gonzalo Mart\'inez-Cervantes

TL;DR
This paper investigates Banach spaces with weak*-sequential dual balls, establishing conditions under which this property is preserved in subspaces and quotients, and providing examples like Johnson-Lindenstrauss space and certain $C(K)$ spaces.
Contribution
It proves that weak*-sequential dual ball property is stable under certain subspace and quotient conditions, and identifies new examples of such spaces.
Findings
Johnson-Lindenstrauss space $JL_2$ has weak*-sequential dual ball
$C(K)$ spaces for scattered compact $K$ of countable height have weak*-sequential dual ball
The property is preserved under subspaces and quotients with the same property
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 is a Banach space with weak*-sequentially compact dual ball and is a subspace such that and have weak*-sequential dual ball, then has weak*-sequential dual ball. As an application we obtain that the Johnson-Lindenstrauss space and for 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.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Advanced Operator Algebra Research
