Operator interpretation of the resonances generated by ${2}\times {2}$ matrix Hamiltonians

An analytic continuation of the transfer function for a $2\times 2$ matrix Hamiltonian to unphysical sheets of the Riemann energy surface is considered. Nonselfadjoint operators are constructed such that their spectra reproduce certain parts of the transfer-function spectrum including resonances on the unphysical sheets nearest to the physical one. The basis property and completeness of the systems of transfer-function root vectors, which include resonance vectors, are established.