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Quasi-minimality and tightness by range in spaces with unconditional basis

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Abstract

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e., of type (4) in the Ferenczi-Rosendal list within the framework of Gowers’ classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with an asymptotically unconditional basis.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, 15780, Greece

    Spiros A. Argyros

  2. Department of Sciences, Technical University of Crete, GR, Chania, 73100, Greece

    Antonis Manoussakis

  3. Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

    Anna Pelczar-Barwacz

Authors
  1. Spiros A. Argyros
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  2. Antonis Manoussakis
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  3. Anna Pelczar-Barwacz
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Corresponding author

Correspondence to Spiros A. Argyros.

Additional information

Research partially supported by the program “Aριστ∈ια” no. 68/1137.

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Argyros, S.A., Manoussakis, A. & Pelczar-Barwacz, A. Quasi-minimality and tightness by range in spaces with unconditional basis. Isr. J. Math. 200, 19–38 (2014). https://doi.org/10.1007/s11856-014-0004-8

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  • DOI: https://doi.org/10.1007/s11856-014-0004-8

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