{
  "abstract": "In this paper, we consider operators that are compositions of an isometric isomorphism and a left multiplier on a Banach algebra, and we provide necessary and sufficient conditions for these operators to have a dense set of periodic elements. As an application of this result, we characterize generalized weighted shifts with a dense set of periodic elements on the standard Hilbert module over C*-algebra of compact operators on a separable Hilbert space. As another application, we characterize generalized weighted shifts with a dense set of periodic elements on the standard Hilbert module over commutative non-unital C*-algebra. Finally, in the last section of the paper, we provide extensions of these results from the case of a sequence generated by powers of a single operator to families of operators indexed over a countable set.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29525",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefan Ivkovic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfmbaq9npdzkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29525",
  "fulltext_url": null,
  "id": "bfmbaq9npdzkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29525",
  "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",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7166638356",
  "pdf_url": "https://arxiv.org/pdf/2606.29525",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bfmbaq9npdzkb.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.29525",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29525"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Periodicity in Banach algebras",
  "title_text": "Periodicity in Banach algebras",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/bfmbaq9npdzkb",
  "venue": "arXiv",
  "versions": []
}