{
  "id": "math/0207064",
  "version": "v1",
  "published": "2002-07-06T19:26:11.000Z",
  "updated": "2002-07-06T19:26:11.000Z",
  "title": "Weyl's theorem, a-Weyl's theorem, and local spectral theory",
  "authors": [
    "Raul E. Curto",
    "Young Min Han"
  ],
  "comment": "23 pages",
  "journal": "J. London Math. Soc. (2) 67(2003), 499-509",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "We give necessary and sufficient conditions for a Banach space operator with the single valued extension property (SVEP) to satisfy Weyl's theorem and $a$-Weyl's theorem. We show that if $T$ or $T^{\\ast}$ has SVEP and $T$ is transaloid, then Weyl's theorem holds for $f(T)$ for every $f\\in H(\\sigma (T))$. When $T^{\\ast}$ has SVEP, $T$ is transaloid and $T$ is $a$-isoloid, then $a$-Weyl's theorem holds for $f(T)$ for every $f\\in H(\\sigma (T))$. We also prove that if $T$ or $T^{\\ast}$ has SVEP, then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-07-06T19:26:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A53",
      "47A11"
    ],
    "keywords": [
      "local spectral theory",
      "a-weyls theorem",
      "weyls theorem holds",
      "essential approximate point spectrum",
      "spectral mapping theorem holds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......7064C"
    }
  }
}