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 2023-03, Vol.46 (2), Article 84
Main Authors: Berasategui, Miguel, Berná, Pablo M., Chu, Hùng Việt
Format: Article
Language:English
Subjects:
Applications of Mathematics
Banach spaces
Mathematics
Mathematics and Statistics
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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