ON THE SPECTRAL PROPERTIES OF THE MODEL OPERATOR ON A FERMIONIC FOCK SPACE

We study a model operator , associated to a system of two identical fermions and another particle of a different nature, acting in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space. We show that the essential spectrum of this operator consist of the union of at most four segments on the real axis. We also explicitely derive a formula for the corresponding resolvent operator.