Weight-Almost Greedy Bases

S. J. Dilworth; Denka Kutzarova; Vladimir Temlyakov; Ben Wallis

doi:10.1134/S0081543818080102

Weight-Almost Greedy Bases

S. J. Dilworth
, Denka Kutzarova
, Vladimir Temlyakov
, Ben Wallis

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	109-128
Number of pages	20
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	303
Issue number	1
DOIs	https://doi.org/10.1134/S0081543818080102
State	Published - Nov 1 2018

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1134/S0081543818080102

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title = "Weight-Almost Greedy Bases",

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.",

author = "Dilworth, \{S. J.\} and Denka Kutzarova and Vladimir Temlyakov and Ben Wallis",

note = "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. Thanks to Pablo M. Bern{\'a} for improving Theorem 5.6.",

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AU - Dilworth, S. J.

AU - Kutzarova, Denka

AU - Temlyakov, Vladimir

AU - Wallis, Ben

N1 - 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. Thanks to Pablo M. Berná for improving Theorem 5.6.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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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JF - Proceedings of the Steklov Institute of Mathematics

IS - 1

ER -

Weight-Almost Greedy Bases

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