{
  "abstract": "A closed subspace $E$ of a Banach space $F$ is \\emph{$L$-embedded in $F$} if there is a projection $P\\colon F\\to E$ such that $\\|x\\|=\\|Px\\|+\\|x-Px\\|$ for all $x\\in F$. We show that if $X$ is a proper, geodesic metric space with locally finite $\\H^1$-measure, then its Lipschitz-free space, denoted by $\\F(X)$, is $L$-embedded in its bidual. We also extend an argument by Cúth, Kalenda, and Kaplický, to show that if $E$ is a finite dimensional normed space and $C\\ge 1$ is such that every subspace of $E$ is $C$-complemented in $E$, then $\\cal F(E)$ is $C$-complemented in its bidual. In particular, for every two-dimensional normed space $E$, $\\cal F(E)$ is $1$-complemented in its bidual.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18608",
  "author_total": 6,
  "authors": [
    {
      "name": "Bruno M. Braga"
    },
    {
      "name": "Chris Gartland"
    },
    {
      "name": "Gilles Lancien"
    },
    {
      "name": "Eva Pernecká"
    },
    {
      "name": "Pavlos Motakis"
    },
    {
      "name": "Thomas Schlumprecht"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f6nd5cjd5ea5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18608",
  "fulltext_url": null,
  "id": "7f6nd5cjd5ea5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18608",
  "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",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7221781613",
  "pdf_url": "https://arxiv.org/pdf/2610.18608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f6nd5cjd5ea5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18608"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On complementation and $L$-embedding of Lipschitz-free spaces in their biduals",
  "title_text": "On complementation and L-embedding of Lipschitz-free spaces in their biduals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/7f6nd5cjd5ea5",
  "venue": "arXiv",
  "versions": []
}