Finite Operators and Weyl Type Theorems for Quasi-*-n-Paranormal Operators

Abstract

Abstract. In this paper, we mainly obtain the following assertions: (1) If T is a quasi- * -n-paranormal operator, then T is finite and simply polaroid. (2) If T or T * is a quasi- * -nparanormal operator, then Weyl's theorem holds for f (T ), where f is an analytic function on σ(T ) and is not constant on each connected component of the open set U containing σ(T ). (3) If E is the Riesz idempotent for a nonzero isolated point λ of the spectrum of a quasi- * -n-paranormal operator, then E is self-adjoint and EH = N (T − λ) = N (T − λ) * .