The separable quotient problem and the strongly normal sequences

Abstract

We study the notion of a strongly normal sequence in the dual E^* of a Banach space E. In particular, we prove that the following three conditions are equivalent:
(1) E^* has a strongly normal sequence,
(2) (E^*, σ(E^*,E)) has a Schauder basic sequence,
(3) E has an infinite-dimensional separable quotient.