{
  "id": "math/0610885",
  "version": "v1",
  "published": "2006-10-28T22:33:49.000Z",
  "updated": "2006-10-28T22:33:49.000Z",
  "title": "Generalized Browder's and Weyl's Theorems for Banach space operators",
  "authors": [
    "Raul E. Curto",
    "Young Min Han"
  ],
  "journal": "J. Math. Anal. Appl. 336(2007), 1424-1442.",
  "categories": [
    "math.FA",
    "math.SP"
  ],
  "abstract": "We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem, and we obtain new necessary and sufficient conditions to guarantee that the spectral mapping theorem holds for the B-Weyl spectrum and for polynomials in T. We also prove that the spectral mapping theorem holds for the B-Browder spectrum and for analytic functions on an open neighborhood of \\sigma(T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f \\in H(T), the space of functions analytic on an open neighborhood of \\sigma(T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f \\in H(\\sigma(T)).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-28T22:33:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A10",
      "47A53",
      "47B20"
    ],
    "keywords": [
      "banach space operator",
      "spectral mapping theorem holds",
      "open neighborhood",
      "sufficient conditions",
      "generalized browders theorem holds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jmaa.2007.03.060",
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2007,
      "month": "Dec",
      "volume": 336,
      "number": 2,
      "pages": 1424
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JMAA..336.1424C"
    }
  }
}