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    A Subspace of l2(X) without the approximation property

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    Date

    2012-11-10

    Author

    Chlebovec, Christopher

    Degree

    M.Sc.

    Discipline

    Mathematical Sciences

    Subject

    Mathematics
    Banach algebras

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    Abstract

    The aim of the thesis is to provide support to the following conjecture, which would provide an isomorphic characterization of a Hilbert space in terms of the approximation property: an infinite dimensional Banach space X is isomorphic to l₂ if and only if every subspace of l₂ (X) has the approximation property. We show that if X has cotype 2 and the sequence of Euclidean distances {dn(X *)}n of X * satisfies dn (X *) ≥ α(log2 n )β for all n ≥ 1 and some absolute constants α > 0 and β > 4, then [cursive l] 2 (X ) contains a subspace without the approximation property.

    URI

    http://knowledgecommons.lakeheadu.ca/handle/2453/149

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