{
  "abstract": "For a locally convex space $L$ let $L'_σ$ denote its dual endowed with the weak* topology $σ(L',L)$. We prove that $L'_σ$ is hemicompact if and only if $L$ with the Mackey topology $τ(L,L')$ is metrizable and barrelled, and if and only if $L'_σ$ is $σ$-compact and quasi-complete. The key step is that a hemicompact $L'_σ$ is quasi-complete. The Mackey topology $τ(L,L')$ is metrizable if and only if $L'$ is a countable union of absolutely convex weak*-compact sets; spaces with normable barrelled Mackey topology are characterized similarly. As a consequence, a metrizable (in particular, normed) space $L$ is barrelled if and only if $L'_σ$ is hemicompact. For function spaces we obtain: $(C_k(X))'_σ$ is hemicompact if and only if $X$ is hemicompact, and $(C_p(X))'_σ$ is hemicompact if and only if $X$ is countable and all compact subsets of $X$ are finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24615",
  "author_total": 1,
  "authors": [
    {
      "name": "Evgenii Reznichenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1avj3b37qr51e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24615",
  "fulltext_url": null,
  "id": "1avj3b37qr51e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24615",
  "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"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223001225",
  "pdf_url": "https://arxiv.org/pdf/2610.24615",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1avj3b37qr51e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24615",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24615"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Locally convex spaces with hemicompact weak* dual",
  "title_text": "Locally convex spaces with hemicompact weak* dual",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1avj3b37qr51e",
  "venue": "arXiv",
  "versions": []
}