Abstract. In this paper we consider several similarity-invariant classes of operators on a complex Hilbert space. A complete description, in terms of properties of various parts of the spectrum, is obtained for the operators in the closure and for the operators in the interior of each of these classes.
AMS Subject Classification
(1991): 47A58, 47A56, 47L30
Received November 14, 2008, and in revised form May 10, 2010. (Registered under 55/2008.)