Unitary, self-adjoint and ᵊ5-symmetric weighted composition operators on Fock-Sobolev spaces

Abstract

In this paper, we characterize the boundedness and compactness for weighted composition operators on the Fock-Sobolev space F p,m (C n ) , 0 < p < ∞ . We prove that no nontrivial unitary or self-adjoint weighted composition operators exist on F 2,m (C n ) when m 1 . As an application, we also prove that there exist only trivial J -symmetric weighted composition operators on F 2,m (C n ) when m 1 .