Weight-Almost Greedy Bases

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...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2018-11, Vol.303 (1), p.109-128
Main Authors: Dilworth, S. J., Kutzarova, Denka, Temlyakov, Vladimir, Wallis, Ben
Format: Article
Language:English
Subjects:
Banach spaces
Mathematics
Mathematics and Statistics
Weight
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Summary: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543818080102