{
  "id": "2403.19855",
  "version": "v1",
  "published": "2024-03-28T22:04:19.000Z",
  "updated": "2024-03-28T22:04:19.000Z",
  "title": "Spaceability of sets of non-injective maps",
  "authors": [
    "Mikaela Aires",
    "Geraldo Botelho"
  ],
  "comment": "12 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Generalizing a recent result on lineability of sets of non-injective linear operators, we prove, for quite general linear spaces $A$ of maps from an arbitraty set to a sequence space, that, for every $0 \\neq f \\in A$, the subset of $A$ of non-injective maps contains an infinite dimensional subspace of $A$ containing $f$. We provide aplications of the main result to spaces of linear operators between quasi-Banach spaces, to spaces of linear operators belonging to an operator ideal, and, in the nonlinear setting, to linear spaces of homogeneous polynomials and to linear spaces of vector-valued Lispshitz functions on metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-28T22:04:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A03",
      "46B87",
      "47B10"
    ],
    "keywords": [
      "spaceability",
      "general linear spaces",
      "infinite dimensional subspace",
      "vector-valued lispshitz functions",
      "non-injective linear operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}