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Hereditarily normaloid operators. (English) Zbl 1097.47005
Among the established permanence properties of completely hereditarily normaloid operators, the author shows that if \(T\) is an operator in this class, then both \(T\) and \(T^*\) have the single-valued extension property at all points which are not in the Weyl spectrum of \(T\). He then exploits this property to study a-Weyl’s theorem and a-Browder’s theorem for operators in this class.

MSC:
47A10 Spectrum, resolvent
47A11 Local spectral properties of linear operators
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