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Isometric Theory for Greedy-Type Properties with Enlarged Greedy Sums
Abstract
For a semi-normalized Markushevich basis, we study isometric almost-greedy inequalities in which a greedy sum of ϕ(m) terms is compared with coordinate projections onto at most m terms. Here ϕ is any strictly increasing map of the nonnegative integers into themselves with ϕ(0)=0. We sandwich ϕ-almost greediness with constant $1$ (ϕ-AG1) between two levels of symmetry for largest coefficients (SLC): ϕ−SLC1 Longrightarrow ϕ−AG1 Longrightarrow weak ϕ−SLC1. Both implications are equivalences if and only if ϕ(1)≤2. We then characterize ϕ-AG1 by the weighted weak ϕ-SLC or a single homogeneous norm inequality, called Property (Fϕ).
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BibTeX
@misc{berasategui2026isometric,
title = {{Isometric Theory for Greedy-Type Properties with Enlarged Greedy Sums}},
author = {Miguel Berasategui and Hung Viet Chu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34686},
eprint = {2610.34686},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34686},
}
RIS
TY - UNPB
TI - Isometric Theory for Greedy-Type Properties with Enlarged Greedy Sums
AU - Miguel Berasategui
AU - Hung Viet Chu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34686
UR - https://arxiv.org/abs/2610.34686
AB - For a semi-normalized Markushevich basis, we study isometric almost-greedy inequalities in which a greedy sum of ϕ(m) terms is compared with coordinate projections onto at most m terms. Here ϕ is any strictly increasing map of the nonnegative integers into themselves with ϕ(0)=0. We sandwich ϕ-almost greediness with constant $1$ (ϕ-AG_1) between two levels of symmetry for largest coefficients (SLC): ϕ−SLC_1 Longrightarrow ϕ−AG_1 Longrightarrow weak ϕ−SLC_1. Both implications are equivalences if and only if ϕ(1)≤2. We then characterize ϕ-AG_1 by the weighted weak ϕ-SLC or a single homogeneous norm inequality, called Property (F_ϕ).
ER -