Abstract
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.
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Notes
Note that \(A>\emptyset \) and \(A < \emptyset \) for any \(A\subset \mathbb {N}\).
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Communicated by Pedro Tradacete.
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The first author was supported by CONICET-PIP 1609 and ANPCyT PICT-2018-04104. The second author was supported by the Grant PID2019-105599GB-I00/AEI/10.13039/501100011033 (Agencia Estatal de Investigación, Spain) and 20906/PI/18 from Fundación Séneca (Región de Murcia, Spain).
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Berasategui, M., Berná, P.M. & Chu, H.V. Extensions and New Characterizations of Some Greedy-Type Bases. Bull. Malays. Math. Sci. Soc. 46, 84 (2023). https://doi.org/10.1007/s40840-023-01472-8
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DOI: https://doi.org/10.1007/s40840-023-01472-8