  By using the thermo entangled state representation we solve the master
equation for a dissipative cavity with Kerr medium to obtain density operators'
infinite operator-sum representation}$\rho (t)
=\sum_{m,n,l=0}^{\infty}M_{m,n,l}\rho_{0}\mathcal{M}_{m,n,l}^{\dagger}.$ It is
noticeable that}$M_{m,n,l}$ is not hermite conjugate to
$\mathcal{M}_{m,n,l}^{\dagger}$, nevertheless the
normalization}$\sum_{m,n,l=0}^{\infty}\mathcal{M}_{nm,,l}^{\dagger}M_{m,n,l}=1$
still holds}, i.e., they are trace-preserving in a general sense. This example
may stimulate further studying if general superoperator theory needs
modification.
