Toeplitz Operators on the Generalized Fock Space in Symmetrically Normed Ideals

In this paper we will give necessary and sufficient conditions for the operator $T_{\nu }^s$ to be in the symmetrically normed ideal ${\mathcal{C}}_{\mathrm{\Phi }}$ for an arbitrary symmetric norming function $\mathrm{\Phi }$ 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 $0<s\le 1$.