{
  "id": "0708.1657",
  "version": "v2",
  "published": "2007-08-13T07:25:54.000Z",
  "updated": "2008-04-30T16:15:45.000Z",
  "title": "Some inequalities for $(α, β)$-normal operators in Hilbert spaces",
  "authors": [
    "Sever S. Dragomir",
    "Mohammad Sal Moslehian"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA",
    "math.OA"
  ],
  "abstract": "An operator $T$ acting on a Hilbert space is called $(\\alpha ,\\beta)$-normal ($0\\leq \\alpha \\leq 1\\leq \\beta $) if \\begin{equation*} \\alpha ^{2}T^{\\ast }T\\leq TT^{\\ast}\\leq \\beta ^{2}T^{\\ast}T. \\end{equation*} In this paper we establish various inequalities between the operator norm and its numerical radius of $(\\alpha ,\\beta)$-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-30T16:15:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A12"
    ],
    "keywords": [
      "hilbert space",
      "normal operators",
      "inner product spaces",
      "operator norm",
      "classical inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.1657D"
    }
  }
}