We introduce the class of $(M, k)$-quasi-$*$-paranormal operators on a Hilbert space $H$. This extends classes $*$-paranormal and $k$-quasi-$*$-paranormal operators. An operator $T$ complex is called if there exists $M>0$ such that \begin{equation*} \sqrt{M}\left\Vert T^{k+2}x\right\Vert \left\Vert T^{k}x\right\Vert \geq T^{\ast }T^{k}x\right\Vert ^{2} \end{equation*} for all $x\in H.$ In prese...

in this article, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $l^{2}(sigma)$ such as, $n$-power normal, $n$-power quasi-normal, $k$-quasi-paranormal and quasi-class$a$. then we show that weighted composition operators can separate these classes.

In this article, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^{2}(Sigma)$ such as, $n$-power normal, $n$-power quasi-normal, $k$-quasi-paranormal and quasi-class$A$. Then we show that weighted composition operators can separate these classes.

In this paper, we introduce a new class of operators, called k−quasi class An operators, which is a superclass of hyponormal operators and a subclass of (n, k)−quasi−∗−paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that, if T ∈ An then σjp(T ) = σp(T ), σja(T ) = σa(T ) and T − λ has finite ascent for all λ ∈ C. Al...