NUMERICAL RANGE OF THE FRIEDRICHS MODEL WITH RANK THREE PERTURBATION

In this paper the Friedrichs model with rank three perturbation, acting in the Hilbert space is considered. This model is a linear, bounded, and self-adjoint and it is a model operator corresponding to the Hamiltonian of the two particle system on the one-dimensional lattice. The numerical range of the considered Friedrichs model is studied by the numerical ranges of the three auxiliary Friedrichs models with rank one perturbation.