{
  "id": "1905.08009",
  "version": "v1",
  "published": "2019-05-20T11:48:28.000Z",
  "updated": "2019-05-20T11:48:28.000Z",
  "title": "Operator norm and numerical radius analogues of Cohen's inequality",
  "authors": [
    "Roman Drnovšek"
  ],
  "comment": "5 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $D$ be an invertible multiplication operator on $L^2(X, \\mu)$, and let $A$ be a bounded operator on $L^2(X, \\mu)$. In this note we prove that $\\|A\\|^2 \\le \\|D A\\| \\, \\|D^{-1} A\\|$, where $\\|\\cdot\\|$ denotes the operator norm. If, in addition, the operators $A$ and $D$ are positive, we also have $w(A)^2 \\le w(D A) \\, w(D^{-1} A)$, where $w$ denotes the numerical radius.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-20T11:48:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A30",
      "47A12",
      "47A10"
    ],
    "keywords": [
      "numerical radius analogues",
      "operator norm",
      "cohens inequality",
      "invertible multiplication operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}