{
  "abstract": "Several useful concepts of almost frames or Riesz bases of Hilbert spaces gave us the motivation to review the theory of C*-module frames and C*-module Riesz bases for Hilbert C*-modules, searching for similar useful structures. We give a survey of the background in C*-module frame theory, summarizing and particularly extending or correcting earlier results. The concepts of near-Riesz bases, pseudo-frames, pseudo-Riesz sequences, and pseudo Riesz bases of Hilbert C*-modules are introduced and equivalently related to (semi-)C*-Fredholm properties of their synthesis operators. The notion of the excess of a C*-module frame is introduced, taking values in related C* algebras. Indicators for possible erasures of frame elements are described with the aim to preserve robustness of frames. Introducing a new notion of pseudo-Riesz-Weyl sequences in the standard Hilbert C*-module $l_2(A)$ we reverse the found correspondence by assuming the associated synthesis operator of a Bessel sequence to be (upper semi-)C*-Weyl. Furthermore, we deduce from the invariance of (upper semi-)C*-Fredholm and C*-Riesz-Weyl properties of synthesis operators with respect to ''compact'' perturbations the perturbation invariance of the respective classes of module Bessel sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.16597",
  "author_total": 2,
  "authors": [
    {
      "name": "Michael Frank"
    },
    {
      "name": "Stefan Ivkovic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bfr0p0kzrrne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.16597",
  "fulltext_url": null,
  "id": "7bfr0p0kzrrne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.16597",
  "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/2606.16597",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bfr0p0kzrrne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2606.16597",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.16597"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Near-Riesz and pseudo-Riesz bases of Hilbert C*-modules and semi-C*-Fredholm operators",
  "title_text": "Near-Riesz and pseudo-Riesz bases of Hilbert C*-modules and semi-C*-Fredholm operators",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/7bfr0p0kzrrne",
  "venue": "arXiv",
  "versions": []
}