The single valued extension property for hereditarily normaloid operators (Q2842091)

A bounded linear operator \(T\) on a complex Hilbert space is said to be hereditarily normaloid if the restriction of \(T\) to any of its closed invariant subspaces \({\mathcal M}\) is normaloid, i.e., the norm of \(T|_{{\mathcal M}}\) equals its spectral radius. The authors show that every hereditarily normaloid operator has the single-valued extension property, and provide an example of a hereditarily normaloid operator which does not satisfy Weyl's theorem. For related results, the reader may consult [\textit{B. P. Duggal} et al., Acta Sci. Math. 71, No. 1--2, 337--352 (2005; Zbl 1106.47016)].