# Spectrum of k-quasi-class A_n operators

## Keywords:

Class $A_n$, $k$-quasi-class $A_n$, Fuglede-Putnam Theorem, Riesz Idempotent, Polaroid Operators## Abstract

In this paper, we introduce a new class of operators, called $k$-quasi-class $A_n$ operators, which is a superclass of class $A$ and a subclass of $(n,k)$-quasiparanormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that, if $T$ is of $k$-quasi-class $A_n$ then $T-\lambda$ has finite ascent for all $\lambda\in\c$. Also, we will prove $T$ is polaroid and Weyl's theorem holds for $T$ and $f(T)$, where $f$ is an analytic function in a neighborhood of the spectrum of $T$. Moreover, we show that if $\lambda$ is an isolated point of $\s(T)$ and $E$ is the Riesz idempotent of the spectrum of a $k$-quasi-class $A_n$ operator $T$, then $E\h=\n(T-\lambda)$ if $\lambda\neq 0$ and $E\h=\n(T^{n+1})$ if $\lambda=0$.

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## How to Cite

*New Zealand Journal of Mathematics*,

*50*, 61–70. Retrieved from https://nzjmath.org/index.php/NZJMATH/article/view/64