Mathematische Annalen

, Volume 335, Issue 3, pp 687–715 | Cite as

Biorthogonal systems and quotient spaces via baire category methods

  • Stevo Todorcevic


We show that every Banach space X of density smaller that the Baire category number Open image in new window admits a quotient with a long Schauder basis that can be taken of length ω1 if X is not separable. So, assuming that the Baire category number Open image in new window does not take its minimal possible value, a Banach space X is separable if and only if all biorthogonal systems of X are countable.


Banach Space Category Method Quotient Space Category Number Baire Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Université Paris 7 -C.N.R.S., UMR 7056Paris Cedex 05France

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