{
  "id": "1501.01897",
  "version": "v1",
  "published": "2015-01-08T16:24:01.000Z",
  "updated": "2015-01-08T16:24:01.000Z",
  "title": "Essential Spectra of Induced Operators on Subspaces and Quotients",
  "authors": [
    "D. C. Moore"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a complex Banach space and let $T$ be a bounded linear operator on $X$. For any closed $T$-invariant subspace $F$ of $X$, $T$ induces operators $T_{|F}:F \\longrightarrow F$ and $T/F:X/F\\longrightarrow X/F$. In this note, we give a simple proof of the fact that the essential spectra of $T_{|F}$ and $T/F$ are always contained in the polynomial hull of the essential spectrum of $T$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-08T16:24:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A53"
    ],
    "keywords": [
      "essential spectrum",
      "induced operators",
      "complex banach space",
      "polynomial hull",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}