A note on *-paranormal operators and related classes of operators

Abstract

We shall show that the Riesz idempotent Eλ of every *- paranormal operator T on a complex Hilbert space H with respect to each isolated point λ of its spectrum σ(T) is self-adjoint and satisfies Eλ H = ker(T - λ) = ker(T - λ)*. Moreover, Weyl's theorem holds for *-paranormal operators and more general for operators T satisfying the norm condition Finally, for this more general class of operators we find a sufficient condition such that EλH = ker(T - λ) = ker(T - λ)* holds. © 2014 Korean Mathematical Society.