{
  "id": "1204.2623",
  "version": "v1",
  "published": "2012-04-12T06:33:13.000Z",
  "updated": "2012-04-12T06:33:13.000Z",
  "title": "(E,F)-multipliers and applications",
  "authors": [
    "Fedor Sukochev",
    "Anna Tomskova"
  ],
  "comment": "16 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For two given symmetric sequence spaces $E$ and $F$ we study the $(E,F)$-multiplier space, that is the space all of matrices $M$ for which the Schur product $M\\ast A$ maps $E$ into $F$ boundedly whenever $A$ does. We obtain several results asserting continuous embedding of $(E,F)$-multiplier space into the classical $(p,q)$-multiplier space (that is when $E=l_p$, $F=l_q$). Furthermore, we present many examples of symmetric sequence spaces $E$ and $F$ whose projective and injective tensor products are not isomorphic to any subspace of a Banach space with an unconditional basis, extending classical results of S. Kwapie\\'{n} and A. Pe{\\l}czy\\'{n}ski and of G. Bennett for the case when $E=l_p$, $F=l_q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-12T06:33:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric sequence spaces",
      "multiplier space",
      "applications",
      "unconditional basis",
      "injective tensor products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2623S"
    }
  }
}