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Axioms of determinacy and biorthogonal systems

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Abstract

If allΠ 1 n games are determined, every non-norm-separable subspaceX ofl ∞(N) which is W* —Σ +1/1 n contains a biorthogonal system of cardinality 2ℵ 0. In Levy’s model of Set Theory, the same is true of every non-norm-separable subspace ofl ∞(N) which is definable from reals and ordinals. Under any of the above assumptions,X has a quotient space which does not linearly embed into 1∞(N).

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Authors and Affiliations

  1. Centre National de la Recherche Scientifique and Equipe d’Analyse, Université Paris VI, Tour 46-0, 4ème étage, 4, Place Jussieu, 75952, Paris Cedex 05, France

    Gilles Godefroy & Alain Louveau

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  1. Gilles Godefroy
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  2. Alain Louveau
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Godefroy, G., Louveau, A. Axioms of determinacy and biorthogonal systems. Israel J. Math. 67, 109–116 (1989). https://doi.org/10.1007/BF02764903

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