Toeplitz Operators on the Generalized Fock Space in Symmetrically Normed Ideals

Abstract

In this paper we will give necessary and sufficient conditions for the operator $T_\nu^s$ to be in the symmetrically normed ideal $\mathcal{C}_\Phi$ for an arbitrary symmetric norming function $\Phi$ where $T_\nu$ is the Toeplitz operator on the generalized Fock Space (also known as the generalized Bargmann-Fock space) with a positive measure symbol $\nu$ and $0<s\leq 1$.