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Biorthogonal systems and quotient spaces via baire category methods

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We show that every Banach space X of density smaller that the Baire category number 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 does not take its minimal possible value, a Banach space X is separable if and only if all biorthogonal systems of X are countable.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, M5S 3G3, Canada

    Stevo Todorcevic

  2. Université Paris 7 -C.N.R.S., UMR 7056, 2, Place Jussieu, Case 7012, 75251, Paris Cedex 05, France

    Stevo Todorcevic

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  1. Stevo Todorcevic
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Correspondence to Stevo Todorcevic.

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Todorcevic, S. Biorthogonal systems and quotient spaces via baire category methods. Math. Ann. 335, 687–715 (2006). https://doi.org/10.1007/s00208-006-0762-7

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  • DOI: https://doi.org/10.1007/s00208-006-0762-7

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