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On uniqueness and plentitude of subsymmetric sequences

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Abstract

We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(T*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(T*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some \({\ell _p}\) or c0.

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Acknowlegement

We thank the referee for their helpful comments and suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211-4100, USA

    Peter G. Casazza

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Stephen J. Dilworth

  3. Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, IL, 61807, USA

    Denka Kutzarova

  4. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, 1113, Bulgaria

    Denka Kutzarova

  5. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Pavlos Motakis

Authors
  1. Peter G. Casazza
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  2. Stephen J. Dilworth
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  3. Denka Kutzarova
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  4. Pavlos Motakis
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Corresponding author

Correspondence to Stephen J. Dilworth.

Additional information

The first author was supported by NSF DMS 1906025.

The second author was supported by Simons Foundation Collaboration Grant No. 849142.

The third author was supported by Simons Foundation Collaboration Grant No. 636954.

The fourth author was supported by NSERC Grant RGPIN-2021-03639.

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Casazza, P.G., Dilworth, S.J., Kutzarova, D. et al. On uniqueness and plentitude of subsymmetric sequences. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2589-2

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  • DOI: https://doi.org/10.1007/s11856-023-2589-2

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