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Weight-Almost Greedy Bases

Proceedings of the Steklov Institute of Mathematics volume 303, pages 109–128 (2018)Cite this article

Abstract

We introduce the notion of a weight-almost greedy basis and show that a basis for a real Banach space is w-almost greedy if and only if it is both quasi-greedy and w-democratic. We also introduce the notion of a weight-semi-greedy basis and show that a w-almost greedy basis is w-semi-greedy and that the converse holds if the Banach space has finite cotype.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, 1523 Greene St., Columbia, SC, 29208, USA

    S. J. Dilworth & Vladimir Temlyakov

  2. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, IL, 61801, USA

    Denka Kutzarova

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev St., Sofia, 1113, Bulgaria

    Denka Kutzarova

  4. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Vladimir Temlyakov

  5. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    Vladimir Temlyakov

  6. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, 60115-2888, USA

    Ben Wallis

Authors
  1. S. J. Dilworth
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  2. Denka Kutzarova
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  3. Vladimir Temlyakov
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  4. Ben Wallis
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Corresponding authors

Correspondence to S. J. Dilworth, Denka Kutzarova, Vladimir Temlyakov or Ben Wallis.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Vol. 303, pp. 120–141.

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Dilworth, S.J., Kutzarova, D., Temlyakov, V. et al. Weight-Almost Greedy Bases. Proc. Steklov Inst. Math. 303, 109–128 (2018). https://doi.org/10.1134/S0081543818080102

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  • DOI: https://doi.org/10.1134/S0081543818080102