Difference of weighted composition operators between some spaces of analytic function spaces

Abstract

We first obtain a simpler proof of the main results in [IEOT, {\bf 93}(2021), 17], which characterized the bounded and compact differences $C_{u,\ddot{I}†}-C_{v,\ddot{I}ˆ}$ of two weighted composition operators acting between different Bergman spaces. More importantly, we get some characterizations for the difference of two weighted composition operators belonging to Schatten class. Futhermore, the compact difference of two weighted composition operators acting on Hardy-Hilbert spaces is also studied.