{
  "abstract": "Let $Y$ be a closed subspace of a real Banach space $X$. Let $(Ω,Σ,μ)$ be a complete finite measure space and let $1<p<\\infty$. We prove that $Y$ has property-$(U)$, property-$(SU)$, property-$(wU)$ in $X$ if and only if $L^p(μ,Y)$ has the corresponding property in $L^p(μ,X)$. No Radon-Nikodým assumption on $X^*$ is required. The proofs use $w^*$-measurable representations of dual functionals and a simultaneous scalar-lifting construction. A norm-minimal representation for an element in $L^p(μ,X)^*$ is found suitable in this case. We also study the point of continuity of the identity map under different topologies on the unit sphere of $L^p(μ,X)^*$. For Bochner-integrable functionals, the pointwise $w^*-w$-continuity yields the uniqueness of the extension to $L^p(μ,X^{**})$. Examples show why arbitrary $w^*$-measurable representatives cannot replace the norm-minimal representatives in this context.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03203",
  "author_total": 2,
  "authors": [
    {
      "name": "Sainik Karak"
    },
    {
      "name": "Tanmoy Paul"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vkn3qpp7vyjj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03203",
  "fulltext_url": null,
  "id": "1vkn3qpp7vyjj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03203",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vkn3qpp7vyjj.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unique Hahn-Banach extensions in Bochner $L^p$ spaces",
  "title_text": "Unique Hahn-Banach extensions in Bochner L^p spaces",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/1vkn3qpp7vyjj",
  "venue": "arXiv",
  "versions": []
}