Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

Tom 163 / 2004

Studia Mathematica 163 (2004), 85-101 MSC: 47A53, 47A10, 47B20. DOI: 10.4064/sm163-1-5

Streszczenie

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.