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