{
  "id": "math/9404210",
  "version": "v1",
  "published": "1994-04-14T16:07:37.000Z",
  "updated": "1994-04-14T16:07:37.000Z",
  "title": "Orlicz property of operator spaces and eigenvalue estimates",
  "authors": [
    "Marius Junge"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators \\[ \\summ_k || Tx_k || \\leq c || \\summ_k e_k \\otimes x_k ||_{\\ell_1\\otimes_{min}E}\\] in the category of operator spaces, it turns out that there are quite different interesting examples of 1 summing operator spaces. Moreover, the eigenvalues of a composition $TS$ decreases of order $n^{\\frac{1}{q}}$ for all operators $S$ factorizing completely through a commutative $C^*$-algebra if and only if the 1 summing norm of the operator $T$ restricted to a $n$-dimensional subspace is not larger than $c n^{1-\\frac{1}{q}}$, provided $q>2$. This notion of 1 summing operators is closely connected to the notion of minimal and maximal operator spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-04-14T16:07:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eigenvalue estimates",
      "orlicz property",
      "finite dimensional banach spaces",
      "maximal operator spaces",
      "unconditional convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1994math......4210J"
    }
  }
}