{
  "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 $1$ ($ϕ$-AG$_1$) between two levels of symmetry for largest coefficients (SLC): $$ϕ\\mbox{-SLC}_1\\ \\Longrightarrow\\ ϕ\\mbox{-AG}_1\\ \\Longrightarrow\\ \\mbox{weak }ϕ\\mbox{-SLC}_1.$$ Both implications are equivalences if and only if $ϕ(1)\\le2$. We then characterize $ϕ$-AG$_1$ by the weighted weak $ϕ$-SLC or a single homogeneous norm inequality, called Property $(F_ϕ)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34686",
  "author_total": 2,
  "authors": [
    {
      "name": "Miguel Berasategui"
    },
    {
      "name": "Hung Viet Chu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rffd2r9w775v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34686",
  "fulltext_url": null,
  "id": "9rffd2r9w775v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34686",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7224026680",
  "pdf_url": "https://arxiv.org/pdf/2610.34686",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9rffd2r9w775v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34686",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34686"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Isometric Theory for Greedy-Type Properties with Enlarged Greedy Sums",
  "title_text": "Isometric Theory for Greedy-Type Properties with Enlarged Greedy Sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9rffd2r9w775v",
  "venue": "arXiv",
  "versions": []
}