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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 303, Pages 120–141
DOI: https://doi.org/10.1134/S0371968518040106 (Mi tm3956) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Weight-almost greedy bases

S. J. Dilwortha, D. Kutzarovabc, V. N. Temlyakovade, B. Wallisf

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
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DOI: https://doi.org/10.1134/S0371968518040106
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.
Funding agency Grant number
National Science Foundation DMS-1361461
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
The first author was supported by the National Science Foundation under grant no. DMS-1361461. The third author was supported by a grant of the Government of the Russian Federation, project no. 14.W03.31.0031. The first and second authors were supported by the Workshop in Analysis and Probability at Texas A&M University in 2017.
Received: February 28, 2018
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 303, Pages 109–128
DOI: https://doi.org/10.1134/S0081543818080102
Bibliographic databases:
Document Type: Article
UDC: 517.982.22
Language: Russian
Citation: S. J. Dilworth, D. Kutzarova, V. N. Temlyakov, B. Wallis, “Weight-almost greedy bases”, Harmonic analysis, approximation theory, and number theory, Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 303, MAIK Nauka/Interperiodica, Moscow, 2018, 120–141; Proc. Steklov Inst. Math., 303 (2018), 109–128
Citation in format AMSBIB
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\paper Weight-almost greedy bases
\inbook Harmonic analysis, approximation theory, and number theory
\bookinfo Collected papers. Dedicated to Academician Sergei Vladimirovich Konyagin on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 303
\pages 120--141
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 4 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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