{
  "id": "2404.05407",
  "version": "v1",
  "published": "2024-04-08T11:15:23.000Z",
  "updated": "2024-04-08T11:15:23.000Z",
  "title": "On vector measures with values in $c_0(κ)$",
  "authors": [
    "José Rodríguez"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $\\nu$ be a vector measure defined on a $\\sigma$-algebra $\\Sigma$ and taking values in a Banach space. We prove that if $\\nu$ is homogeneous and $L_1(\\nu)$ is non-separable, then there is a vector measure $\\tilde{\\nu}:\\Sigma \\to c_0(\\kappa)$ such that $L_1(\\nu)=L_1(\\tilde{\\nu})$ with equal norms, where $\\kappa$ is the density character of $L_1(\\nu)$. This is a non-separable version of a result of [G.P. Curbera, Pacific J. Math. 162 (1994), no. 2, 287--303].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-08T11:15:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector measure",
      "banach space",
      "equal norms",
      "density character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}