Extensions and New Characterizations of Some Greedy-Type Bases

Partially greedy bases in Banach spaces were introduced by Dilworth et al. as a strictly weaker notion than the (almost) greedy bases. In this paper, we study two natural ways to strengthen the definition of partial greediness. The first way produces what we call the consecutive almost greedy proper...

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Bibliographic Details
Published in:	Bulletin of the Malaysian Mathematical Sciences Society Vol. 46; no. 2
Main Authors:	Berasategui, Miguel, Berná, Pablo M., Chu, Hùng Việt
Format:	Journal Article
Language:	English
Published:	Singapore Springer Nature Singapore 01-03-2023 Springer Nature B.V
Subjects:	Applications of Mathematics Banach spaces Mathematics Mathematics and Statistics 46B15 Partially greedy Bases Almost greedy 41A65
Online Access:	Get full text
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Summary:	Partially greedy bases in Banach spaces were introduced by Dilworth et al. as a strictly weaker notion than the (almost) greedy bases. In this paper, we study two natural ways to strengthen the definition of partial greediness. The first way produces what we call the consecutive almost greedy property, which turns out to be equivalent to the almost greedy property. Meanwhile, the second way reproduces the PG property for Schauder bases but a strictly stronger property for general bases.
ISSN:	0126-6705 2180-4206
DOI:	10.1007/s40840-023-01472-8