Spectral Relations for a Matrix Model in Fermionic Fock Space

A matrix model $$\mathcal{A}$$ is considered related to a system describing two identical fermions and one particle of another nature on a lattice, interacting via annihilation and creation operators. The problem of the study of the spectrum of a block operator matrix $$\mathcal{A}$$ is reduced to the investigation of the spectrum of block operator matrices of order three with a discrete variable, and the relations for the spectrum, essential spectrum, and point spectrum are established. Two-particle and three-particle branches of the essential spectrum of the block operator matrix $$\mathcal{A}$$ are singled out.

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