Weyl's and Browder's theorems for operators satisfying the SVEP

Tom 163 / 2004

Mourad Oudghiri Studia Mathematica 163(2004), 85-101 MSC: 47A53, 47A10, 47B20. DOI: 10.4064/sm163-1-5 Opublikowany online: 1 January 1970


We study Weyl's and Browder's theorem for an operator $T$ on a Banach space such that $T$ or its adjoint has the single-valued extension property. We establish the spectral mapping theorem for the Weyl spectrum, and we show that Browder's theorem holds for $f(T)$ for every $f\in {\mathcal H}(\sigma (T))$. Also, we give necessary and sufficient conditions for such $T$ to obey Weyl's theorem. Weyl's theorem in an important class of Banach space operators is also studied.


  • Mourad OudghiriUFR de Mathématiques
    UMR-CNRS 8524
    Université Lille 1
    59655 Villeneuve d'Ascq, France

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