Abstract
An interesting result due to Dilworth et al. was that if we enlarge greedy sums by a constant factor \(\lambda > 1\) in the condition defining the greedy property, then we obtain an equivalence of the almost greedy property, a strictly weaker property. Previously, the author showed that enlarging greedy sums by \(\lambda\) in the condition defining the partially greedy (PG) property also strictly weakens the property. However, enlarging greedy sums in the definition of reverse partially greedy (RPG) bases by Dilworth and Khurana again gives RPG bases. The companion of PG and RPG bases suggests the existence of a characterization of RPG bases which, when greedy sums are enlarged, gives an analog of a result that holds for partially greedy bases. In this paper, we show that such a characterization indeed exists, answering positively a question previously posed by the author.
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Acknowledgements
The author is thankful to Timur Oikhberg for helpful comments on an earlier draft of this paper. The author would also like to thank the anonymous referees for a careful reading and constructive feedback that improves the paper’s exposition.
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Chu, H. Larger greedy sums for reverse partially greedy bases. Anal Math (2024). https://doi.org/10.1007/s10476-024-00008-x
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DOI: https://doi.org/10.1007/s10476-024-00008-x