Virtual levels of $n$-particle systems

The energy operators $H$ of unstable quantum systems $Z_1$ that do not possess stable subsystems are considered. It is shown that if the Hamiltonians of the subsystems in $Z_1$ do not have virtual levels but the operator $H$ does then a virtual level of the operator $H$ is due to the existence of a finitedimensional subspace of functions $\mathscr W=\{u\}\in\mathscr L_2^{(1)}$ such that the functions $u$ are generalized solutions of the Schrödinger equation $Hu=0$ and on the subspace orthogonal (in the gradient sense) to $\mathscr W$ the operator $H$ does not have virtual levels.