Lindelof type of generalization of separability in Banach spaces

2008/03/25 by Talponen, Jarno
#46A50 #46B26 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0803.3541

Abstract

We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: For each subset F of X^∗, which separates X, there exists a countable separating subset F₀ of F. All separable Banach spaces have CSP and plenty of examples of non-separable CSP spaces are provided. Connections of CSP with Markucevic-bases, Corson property and related geometric issues are discussed.

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