Upper Triangular Operator Matrices , SVEP and Browder , Weyl Theorems
نویسنده
چکیده
A Banach space operator T ∈ B(X ) is polaroid if points λ ∈ isoσσ(T ) are poles of the resolvent of T . Let σa(T ), σw(T ), σaw(T ), σSF+(T ) and σSF−(T ) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T . For A, B and C ∈ B(X ), let MC denote the operator matrix (
منابع مشابه
Weyl ’ S Theorems and Local Spectral Theory 3
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 ∗ has SVEP and T is transaloid, then Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T )). When T ∗ has SVEP, T is transaloid and T is a-isoloid, then a-Weyl’s theorem holds for f(T ) for every f ∈ H(σ(T ...
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