Integral and Weighted Composition Operators on Fock-type Spaces

Abstract

We study various structures of general Volterra-type integral and weighted composition operators acting between two Fock-type spaces mathcal {F}_{varphi }^p and mathcal {F}_{varphi }^q, where varphi is a radial function growing faster than the function zrightarrow |z|^2/2. The main results show that the unboundedness of the Laplacian of varphi provides interesting results on the topological and spectral structures of the operators in contrast to their actions on Fock spaces, where the Laplacian of the weight function is bounded. We further describe the invertible and unitary weighted composition operators. Finally, we show the spaces support no supercyclic weighted composition operator with respect to the pointwise convergence topology and hence with the weak and strong topologies.