Non-compact perturbation of the spectrum of multipliers given by a special form

In this paper, the change of the spectrum of multiplier $H_0f(x,y)=k_0(x,y)f(x,y)$ for perturbation with non-compact partially integral operators is studied. In addition, the existence of resonance is investigated in the model $H =H_0-(\gamma_1T_1+\gamma_2T_2)$.