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.
Wiesław ŚLIWA. "The separable quotient problem and the strongly normal sequences." J. Math. Soc. Japan 64 (2) 387 - 397, April, 2012. https://doi.org/10.2969/jmsj/06420387