Authors: Todorčević, Stevo 
Title: Biorthogonal systems and quotient spaces via baire category methods
Journal: Mathematische Annalen
Volume: 335
Issue: 3
First page: 687
Last page: 715
Issue Date: 1-Jul-2006
Rank: M21
ISSN: 0025-5831
DOI: 10.1007/s00208-006-0762-7
Abstract: 
We show that every Banach space X of density smaller that the Baire category number [InlineMediaObject not available: see fulltext.] admits a quotient with a long Schauder basis that can be taken of length ω 1 if X is not separable. So, assuming that the Baire category number [InlineMediaObject not available: see fulltext.] does not take its minimal possible value, a Banach space X is separable if and only if all biorthogonal systems of X are countable.
Publisher: Springer Link

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