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.

we give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(c_{omega_1,varphi_1}^*‎ , ‎c_{omega_2,varphi_2}^*)$ on the hilbert space $mathcal{h}$ of analytic functions is supercyclic‎.

let $varphi(z)=z^m, z in mathbb{u}$, for some positive integer $m$, and $c_varphi$ be the composition operator on the bergman space $mathcal{a}^2$ induced by $varphi$. in this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $c^*_varphi c_varphi, c_varphi c^*_varphi$ as well as self-commutator and anti-self-commutators of $c_...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

A Hilbert space operator U is called \textit{universal} (in the sense of Rota) if every similar to a multiple restricted one its invariant subspaces. It follows that \textit{invariant subspace problem} for spaces equivalent statement all minimal subspaces are dimensional. In this article we characterize linear fractional composition operators Cϕf=f∘ϕ have universal translates on both classical ...

We characterize the spectrum and essential spectrum of “essentially linear fractional” composition operators acting on the Hardy space H2(U) of the open unit disc U. When the symbols of these composition operators have Denjoy-Wolff point on the unit circle, the spectrum and essential spectrum coincide. Our work permits us to describe the spectrum and essential spectrum of certain associated wei...