{
  "abstract": "We establish a constructive and quasi-Banach framework for approximation spaces $A_μ^ρ$ of compact $H$-operators between Banach and quasi-Banach spaces. By leveraging delayed Riesz means $V_{2^{bn}}$ generated by self-adjoint differential operators $P(D)$, we replace abstract best approximants with explicit linear operator decompositions. Furthermore, we extend the theory of $H$-operator approximation spaces to quasi-Banach settings ($0 < p < 1$), bypassing the collapse of Peetre's $K$-functional by employing localized moduli of smoothness $ω_φ^r(f,t)_p$. Integrating seminal spectral bounds due to Markus \\cite{M1966} and factorization techniques for operator ideals, we prove that operators belonging to $A_μ^ρ$ possess complete systems of root vectors whose expansions are Abel summable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14381",
  "author_total": 1,
  "authors": [
    {
      "name": "Daniel Akech Thiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c2e8zvfjj3sdm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14381",
  "fulltext_url": null,
  "id": "c2e8zvfjj3sdm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14381",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.14381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c2e8zvfjj3sdm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14381"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$H$-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli",
  "title_text": "H-Operator Approximation Spaces via Delayed Riesz Means and Quasi-Banach Moduli",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/c2e8zvfjj3sdm",
  "venue": "arXiv",
  "versions": []
}