The separable quotient problem and the strongly normal sequences

Wiesław ŚLIWA

doi:10.2969/jmsj/06420387

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April, 2012 The separable quotient problem and the strongly normal sequences

Wiesław ŚLIWA

J. Math. Soc. Japan 64(2): 387-397 (April, 2012). DOI: 10.2969/jmsj/06420387

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.

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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