{
  "id": "1401.0487",
  "version": "v1",
  "published": "2014-01-02T18:02:05.000Z",
  "updated": "2014-01-02T18:02:05.000Z",
  "title": "Spherical Tuples of Hilbert Space Operators",
  "authors": [
    "S. Chavan",
    "D. Yakubovich"
  ],
  "comment": "a version close to final one",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "We introduce and study a class of operator tuples in complex Hilbert spaces, which we call spherical tuples. In particular, we characterize spherical multi-shifts, and more generally, multiplication tuples on RKHS. We further use these characterizations to describe various spectral parts including the Taylor spectrum. We also find a criterion for the Schatten $S_p$-class membership of cross-commutators of spherical $m$-shifts. We show, in particular, that cross-commutators of non-compact spherical $m$-shifts cannot belong to $S_p$ for $p \\le m$. We specialize our results to some well-studied classes of multi-shifts. We prove that the cross-commutators of a spherical joint $m$-shift, which is a $q$-isometry or a $2$-expansion, belongs to $S_p$ if and only if $p > m$. We further give an example of a spherical jointly hyponormal $2$-shift, for which the cross-commutators are compact but not in $S_p$ for any $p <\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-02T18:02:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A13",
      "47B32",
      "46E20"
    ],
    "keywords": [
      "hilbert space operators",
      "spherical tuples",
      "cross-commutators",
      "complex hilbert spaces",
      "multiplication tuples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0487C"
    }
  }
}