### ON THE SPECTRUM OF A FIRST SCHUR COMPLEMENT RELATED WITH A 3X3 OPERATOR MATRIX

#### Abstract

We consider a 3X3 operator matrix (Hamiltonian) associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles. The first Schur complement corresponding to with respect to the certain decomposition of the three-particle cut subspace of Fock space is constructed and its spectrum is studied.

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