{
  "id": "2304.09581",
  "version": "v1",
  "published": "2023-04-19T11:34:59.000Z",
  "updated": "2023-04-19T11:34:59.000Z",
  "title": "On the spaceability of the set of functions in the Lebesgue space $L_p$ which are in no other $L_q$",
  "authors": [
    "Gustavo Araújo",
    "Anderson Barbosa",
    "Anselmo Raposo Jr.",
    "Geivison Ribeiro"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this note we prove that, for $p>0$, $L_{p}[0,1]\\smallsetminus\\bigcup_{q\\in(p,\\infty)}L_{q}[0,1]$ is $(\\alpha,\\mathfrak{c})$-spaceable if, and only if, $\\alpha<\\aleph_{0}$. Such a problem first appears in [V. F\\'avaro, D. Pellegrino, D. Tomaz, Bull. Braz. Math. Soc. \\textbf{51} (2020) 27-46], where the authors get the $(1,\\mathfrak{c})$-spaceability of $L_{p}[0,1]\\smallsetminus\\bigcup_{q\\in(p,\\infty)}L_{q}[0,1]$ for $p>0$. The definitive answer to this problem continued to be sought by other authors, and some partial answers were obtained. The veracity of this result was expected, as a similar result is known for sequence spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-19T11:34:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A03",
      "46B87",
      "46E30"
    ],
    "keywords": [
      "lebesgue space",
      "spaceability",
      "problem first appears",
      "sequence spaces",
      "partial answers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}