{
  "abstract": "Let $\\{P_j\\}$ be a sequence of projections onto the closed subspaces $\\mathcal{M}_j$ of a Hilbert space $\\mathscr{H}$. Consider an infinite sequence $P_{i_1}, P_{i_2}, \\ldots$ with each $P_{i_n} \\in \\{P_1, P_2, \\ldots\\}$, possibly repeating in some order or randomly. The question is: Under what conditions does the sequence $\\{P_{i_n} \\cdots P_{i_2} P_{i_1} x\\}_{n=1}^{\\infty}$ converge strongly or weakly to $Px$ for every $x \\in \\mathscr{H}$, where $P$ is the projection onto the intersection $\\mathcal{M} = \\bigcap_{i=1}^{\\infty} \\mathcal{M}_i$? In this paper, we present some results concerning random products of countably infinitely many projections $\\{P_j\\}_{j=1}^{\\infty}$ that incorporates the notion of an infinite-periodic function. More precisely, we introduce a new class of functions $σ\\colon \\mathbb{N} \\to \\mathbb{N}$, called infinite-periodic functions, and rigorously show that the sequence $\\{T_n x\\}$ defined by \\[ T_1 := P_{σ(1)}\\quad \\mbox{and} \\quad T_n := P_{σ(n)} T_{n-1} \\quad \\text{for all } n \\geq 2, \\] for $x \\in \\mathscr{H}$, converges weakly to $Px$, where $P$ is the projection onto $\\bigcap_{j=1}^{\\infty} \\mathcal{R}(P_j)$. We also provide some technical examples to illustrate our results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13957",
  "author_total": 2,
  "authors": [
    {
      "name": "Rasoul Eskandari"
    },
    {
      "name": "Mohammad Sal Moslehian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nfae2zvqb25d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13957",
  "fulltext_url": null,
  "id": "4nfae2zvqb25d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13957",
  "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"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13957",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nfae2zvqb25d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13957",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13957"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Convergence of Random Products of Projections Under Infinite-Periodic Selections",
  "title_text": "Convergence of Random Products of Projections Under Infinite-Periodic Selections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4nfae2zvqb25d",
  "venue": "arXiv",
  "versions": []
}