{
  "id": "1702.08671",
  "version": "v1",
  "published": "2017-02-28T07:09:30.000Z",
  "updated": "2017-02-28T07:09:30.000Z",
  "title": "On The Absolute Value of The Product and the Sum of Linear Operators",
  "authors": [
    "Mohammed Hichem Mortad"
  ],
  "comment": "11 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $A,B\\in B(H)$. In the present paper, we establish simple and interesting facts on when we have $|A||B|=|B||A|$, $|AB|=|A||B|$, $|A\\pm B|\\leq |A|+|B|$, $||A|-|B||\\leq |A\\pm B|$ and $\\||A|-|B|\\|\\leq \\|A\\pm B\\|$, where $|\\cdot|$ denotes the absolute value (or modulus) of an operator. The results give some other interesting consequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-28T07:09:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A63",
      "47A62",
      "47B15",
      "47B20"
    ],
    "keywords": [
      "absolute value",
      "linear operators",
      "establish simple",
      "interesting facts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}