S. J. Dilworth, D. Kutzarova, V. N. Temlyakov, B. Wallis, “Weight-almost greedy bases”, Trudy Mat. Inst. Steklova, 2018, Volume 303,Pages <nobr>120–141</nobr>

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Trudy Mat. Inst. Steklova, 2018 Volume 303, Pages 120–141 (Mi tm3956)

This article is cited in 4 papers

Weight-almost greedy bases

S. J. Dilworth^a, D. Kutzarova^bc, V. N. Temlyakov^ade, B. Wallis^f

^a Department of Mathematics, University of South Carolina, 1523 Greene St., Columbia, SC 29208, USA
^b Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, IL 61801, USA
^c Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev St., Sofia, 1113, Bulgaria
^d Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
^e Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
^f Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115-2888, USA

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.

UDC: 517.982.22

Received: February 28, 2018

DOI: 10.1134/S0371968518040106

English version: Proceedings of the Steklov Institute of Mathematics, 2018, 303, 109–128

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