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On asymptotic models in Banach Spaces

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Abstract

A well known application of Ramsey’s Theorem to Banach Space Theory is the notion of a spreading model\((\tilde e_i )\) of a normalized basic sequence (x i) in a Banach spaceX. We show how to generalize the construction to define a new creature (e i), which we call an asymptotic model ofX. Every spreading model ofX is an asymptotic model ofX and in most settings, such as ifX is reflexive, every normalized block basis of an asymptotic model is itself an asymptotic model. We also show how to use the Hindman-Milliken Theorem—a strengthened form of Ramsey’s Theorem—to generate asymptotic models with a stronger form of convergence.

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Authors and Affiliations

  1. Department of Pure Mathematics, Queen’s University Belfast, BT7 1NN, Belfast, Northern Ireland, U.K.

    Lorenz Halbeisen

  2. Department of Mathematics, The University of Texas at Austin, 78712-1082, Austin, TX, USA

    Edward Odell

Authors
  1. Lorenz Halbeisen
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  2. Edward Odell
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Correspondence to Lorenz Halbeisen.

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Research supported by NSF.

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Halbeisen, L., Odell, E. On asymptotic models in Banach Spaces. Isr. J. Math. 139, 253–291 (2004). https://doi.org/10.1007/BF02787552

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  • DOI: https://doi.org/10.1007/BF02787552

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