{
  "abstract": "Let $E(X)$ be a Köthe--Bochner space of functions on a $σ$-finite measure space with values in a Banach space $X$. We study bounded operators on $E(X)$ that commute with the operators of multiplication by functions from $L^\\infty$. If $X$ is separable, every such operator acts pointwise by an essentially bounded $L(X)$-valued function. For a nonseparable $X$, a lifting of $L^\\infty$ provides a representation by $L(X,X^{\\star\\star})$-valued functions, and by $L(X)$-valued functions if $X$ is complemented in $X^{\\star\\star}$, with the sharp norm bound if $X$ is a dual space. As an application, we show that if the transformation is aperiodic, then the spectral projections of invertible weighted composition operators with operator-valued weights are operators of multiplication by $L(X)$-valued functions whenever $X$ is separable or complemented in $X^{\\star\\star}$, and that, if moreover the measure is ergodic and $\\dim X = m < \\infty$, the spectrum of such an operator has at most $m$ connected components. Finally, for $L^p(μ;X)$, $1 \\leq p < \\infty$, an aperiodic nonsingular transformation and a weight that is measurable in the operator norm, we prove that the spectral projections are operators of multiplication by projection-valued functions for an arbitrary Banach space $X$, for instance for $X = c_0(Γ)$ with $Γ$ uncountable. The proof uses an inverse-closedness result for the algebra generated by norm-measurable multipliers and the composition operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24853",
  "author_total": 4,
  "authors": [
    {
      "name": "Hulya Duru"
    },
    {
      "name": "Serkan Ilter"
    },
    {
      "name": "Arkady Kitover"
    },
    {
      "name": "Mehmet Orhon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/by1m8wk8g5s3k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24853",
  "fulltext_url": null,
  "id": "by1m8wk8g5s3k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24853",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223066723",
  "pdf_url": "https://arxiv.org/pdf/2610.24853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/by1m8wk8g5s3k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Operators commuting with $L^\\infty$]{Operators commuting with $L^\\infty$ on Köthe--Bochner spaces",
  "title_text": "Operators commuting with L^∞]{Operators commuting with L^∞ on Köthe--Bochner spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/by1m8wk8g5s3k",
  "venue": "arXiv",
  "versions": []
}