{
  "abstract": "We study the rigidity of the orthogonal projections $P_{n}:H^2(\\mathbb{D}^2)\\rightarrow H_{n}$, where $H^{2}(\\mathbb{D}^{2})=\\bigoplus_{n=0}^{\\infty}H_{n}$ and each $H_{n}=H^{2}(z)w^{n}$ is a reducing subspace for $T_{z}$, and we derive properties of the minimal invariant subspaces of $T_{z}^{*}$. Our main result establishes that the nonzero projections of a minimal invariant subspace onto the one-variable Hardy space share a common $t_z^*$-invariant structure. Furthermore, we relate the results obtained to an approach to the invariant subspace problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19311",
  "author_total": 2,
  "authors": [
    {
      "name": "Marcos dos Santos Ferreira"
    },
    {
      "name": "João Marcos Ribeiro do Carmo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/413pdvtqmwa3w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19311",
  "fulltext_url": null,
  "id": "413pdvtqmwa3w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19311",
  "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": "W7213600760",
  "pdf_url": "https://arxiv.org/pdf/2609.19311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/413pdvtqmwa3w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Projections and minimal invariant subspaces in the Hardy space over the bidisk",
  "title_text": "Projections and minimal invariant subspaces in the Hardy space over the bidisk",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/413pdvtqmwa3w",
  "venue": "arXiv",
  "versions": []
}