The separable quotient problem and the strongly normal sequences
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2012
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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) $(E^*;\sigma (E ^*;E))$ has a Schauder basic sequence,
(3) $E$ has an infinite-dimensional separable quotient.
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J. Math. Soc. Japan, 64(2012), 387-397