Spectral properties of Faddeev's equations

The spectral properties for the matrix operators corresponding to the three particle Faddeev equations are investigated. It is shown that these operators have two types of the invariant subspaces. On the subspaces of the first type the operators have the spectrum of the eigenvalues consisting of the three particle Hamiltonian eigenvalues and corresponding eigenfunctions are expressed in terms of the solutions of the Schrödinger equation. On the subspaces of the second type the operators are equivalent to the kinetic energy operator and consequently their eigenfunctions do not correspond to any dynamics of interacting particles.