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On the diameter of the Banach-Mazur set

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Abstract

On every subspace of l ∞(ℕ) which contains an uncountable ω-independent set, we construct equivalent norms whose Banach-Mazur distance is as large as required. Under Martin’s Maximum Axiom (MM), it follows that the Banach-Mazur diameter of the set of equivalent norms on every infinite-dimensional subspace of l ∞(ℕ) is infinite. This provides a partial answer to a question asked by Johnson and Odell.

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  1. Institut de Mathématiques de Jussieu, CNRS-Université Paris 6, 175, rue du Chevaleret, 75013, Paris, France

    Gilles Godefroy

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  1. Gilles Godefroy
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Correspondence to Gilles Godefroy.

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Godefroy, G. On the diameter of the Banach-Mazur set. Czech Math J 60, 95–100 (2010). https://doi.org/10.1007/s10587-010-0021-7

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  • DOI: https://doi.org/10.1007/s10587-010-0021-7

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