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    • Graduate School - MU Theses and Dissertations (MU)
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    • 2009 Dissertations (MU)
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    Asymptotic unconditionality in Banach spaces

    Cowell, Simon, 1977-
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    [PDF] research.pdf (413.4Kb)
    Date
    2009
    Format
    Thesis
    Metadata
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    Abstract
    We show that a separable real Banach space embeds almost isometrically in a space [Upsilon] with a shrinking 1-unconditional basis if and only if lim [subscript n] [subscript arrow] [subscript infinity] [norms] [chi] [group of units] [plus][chi] [group of units] [subscript n] [norms] [equals] lim [subscript n] [subscript arrow] [subscript infinity][nearest integer function] [norms] [chi][group of units] [minus] [chi] [group of units] [subscript n] [norms] whenever [chi] [group of units] [element of][Chi] [group of units] ([chi][group of units][subscript n]) [superscript infinity] [subscript n[equals]₁ is a weak [group of units] - null sequence and both limits exist. If [Chi] is reflexive then [Upsilon] can be assumed reflexive. These results provide the isometric counterparts of recent work of Johnson and Zheng.
    URI
    https://hdl.handle.net/10355/6149
    https://doi.org/10.32469/10355/6149
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
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    • Mathematics electronic theses and dissertations (MU)
    • 2009 MU dissertations - Freely available online

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