On the finiteness of the discrete spectrum of the three-particle Schrödinger operator

The Schrödinger operator $H$ of a three-particle system with two-body interactions in considered. Under the assumptions that two-particle subsystems do not possess any negative eigenvalues and one of the subsystems has a virtual state at the lower bound of the continuous spectrum, the proof of the finiteness of discrete spectrum of operator $H$ is performed.