{
  "id": "math/9610211",
  "version": "v1",
  "published": "1996-10-07T00:00:00.000Z",
  "updated": "1996-10-07T00:00:00.000Z",
  "title": "Kernels of surjections from ${\\cal L}_1$-spaces with an application to Sidon sets",
  "authors": [
    "Nigel J. Kalton",
    "A. Pelczynski"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "If $Q$ is a surjection from $L^1(\\mu)$, $\\mu$ $\\sigma$-finite, onto a Banach space containing $c_0$ then (*) $\\ker Q$ is uncomplemented in its second dual. If $Q$ is a surjection from an ${\\cal L}_1$-space onto a Banach space containing uniformly $\\ell_n^\\infty$ ($n=1,2,\\dots$) then (**) there exists a bounded linear operator from $\\ker Q$ into a Hilbert space which is not 2-absolutely summing. Let $S$ be an infinite Sidon set in the dual group $\\Gamma$ of a compact abelian group $G$. Then $L^1_{\\tilde{S}}(G)=\\{f\\in L^1(G): \\hat{f}(\\gamma)=0$ for $\\gamma\\in S\\}$ satisfies (*) and (**) hence $L^1_{\\tilde{S}}(G)$ is not an ${\\cal L}_1$-space and is not isomorphic to a Banach lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-10-07T00:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B03",
      "43A46"
    ],
    "keywords": [
      "surjection",
      "application",
      "banach space containing",
      "infinite sidon set",
      "compact abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math.....10211K"
    }
  }
}