{
  "id": "2011.11154",
  "version": "v1",
  "published": "2020-11-23T00:41:19.000Z",
  "updated": "2020-11-23T00:41:19.000Z",
  "title": "Pseudospectra and Simultaneous Control",
  "authors": [
    "Maëva Ostermann"
  ],
  "comment": "9 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We prove that, under some conditions, for $N\\ge 10$, $M>0$ and two functions $f$ and $g$ holomorphic in a domain $\\Omega$, we can find two $N\\times N$ matrices $A$ and $B$ with identical pseudospectra such that we have simultaneously $||f(A)||/||f(B)||>M$ and $||g(A)||/||g(B)||>M$. In particular, this is the case if $f(z)=z^n$ and $g(z)=z^m$, where $n,m\\ge2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-23T00:41:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "15A18",
      "15A60"
    ],
    "keywords": [
      "simultaneous control",
      "conditions",
      "holomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}