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Weight-partially greedy bases and weight-property (A)

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Abstract

In this paper, motivated by the notion of w-property (A), we introduce the notions of w-left property (A) and w-right property (A). We prove a characterization of w-partially greedy (w-reverse partially greedy) bases in terms of w-left property (A) (w-right property (A)) and quasi-greediness. We also study conditions on the weight sequences when w-left property (A) and (or) w-right property (A) implies w-property (A).

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Acknowledgements

This work was supported by the Israel Science Foundation (Grant number—137/16). The author is thankful to Gideon Schechtman for many useful discussions. The author would like to thank Pablo M. Berná for his suggestions to improve the constant in the proof of Theorem 2.2 and Proposition 3.14.

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Authors and Affiliations

  1. Department of Mathematics, The Weizmann Institute of Science, 7610001, Rehovot, Israel

    Divya Khurana

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  1. Divya Khurana
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Correspondence to Divya Khurana.

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Communicated by George Androulakis.

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Khurana, D. Weight-partially greedy bases and weight-property (A). Ann. Funct. Anal. 11, 101–117 (2020). https://doi.org/10.1007/s43034-019-00023-2

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  • DOI: https://doi.org/10.1007/s43034-019-00023-2

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