Continuity of the Spectrum on Some Classes of Operators on a Hilbert Space

Let () denote the algebra of operators on a complex infinite dimensional Hilbert space , and let denote the class of ∈ () which are either -hyponormal or log-hyponormal or -quasihyponormal or of class Θ (of Campbell) or -totally paranormal. It is proved that Weyl's theorem holds for , and that the restriction to of the set valued functions the spectrum, the Browder spectrum and the Weyl spectrum is continuous. We prove also that if is a sequence in converging to , then the approximate point spectrum and the essential approximate point spectrum are continuous at