We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form (1− 〈z, w〉)−γ for γ > 0. We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weigh...

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.

In this paper, we estimate essential norms of weighted composition operators and differences two on the Bergman spaces in unit ball.

We study weighted composition operators on Banach spaces over unbounded, locally finite metric spaces. characterize the that are bounded, compact, being bounded below, having closed range, invertible, a (surjective) isometry, and Fredholm. Several examples presented illustrating diversity of such operators.