Journal of the
Korean Mathematical Society JKMS

In this paper, the authors investigate the structure of operators similar to normaloid and transloid operators. In particular, we characterize the interior of the set of operators similar to normaloid (transloid, respectively) operators. This gives a concise spectral condition to determine when an operator is similar to a normaloid or transloid operator. Also it is proved that any Hilbert space operator has a compact perturbation with transloid property. This is used to give a negative answer to a problem posed by W. Y. Lee, concerning Weyl's theorem.

Keywords: normaloidity, transloid operators, similarity, numerical radius, spectral sets

MSC numbers: Primary 47A12, 47A58; Secondary 47A10, 47A25