Unbounded Weighted Composition Operators on Fock space

TL;DR

This paper studies unbounded weighted composition operators on Fock space, analyzing their properties like selfadjointness, Hermitian, normality, and invertibility, and provides detailed spectrum computations.

Contribution

It introduces new results on the properties and spectrum of unbounded weighted composition operators on Fock space, including their relation to alC-selfadjoint operators.

Findings

Unbounded normal weighted composition operators are properly contained within alC-selfadjoint operators.

Spectrum of these operators is explicitly computed.

Characterization of invertibility and other properties for these operators.

Abstract

In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations), Hermitian, normal, cohyponormal, and invertible. In addition, the paper shows that unbounded normal weighted composition operators are contained properly in the class of $\calC$-selfadjoint operators with respect to weighted composition conjugations. The computation of the spectrum is carried out in detail.