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The spectral problem $(A + V(z))\psi=z\psi$ is considered where the mainHamiltonian $A$ is a self-adjoint operator of sufficiently arbitrary nature.The perturbation $V(z)=-B(A'-z)^{-1}B^{*}$ depends on the energy $z$ asresolvent of another self-adjoint operator $A'$. The latter is usuallyinterpreted as Hamiltonian describing an internal structure of physical system.The operator $B$ is assumed to have a finite Hilbert-Schmidt norm. Theconditions are formulated when one can replace the perturbation $V(z)$ with anenergy-independent ``potential'' $W$ such that the Hamiltonian $H=A +W$ has thesame spectrum (more exactly a part of spectrum) and the same eigenfunctions asthe initial spectral problem. The Hamiltonian $H$ is constructed as a solutionof the non-linear operator equation $H=A+V(H)$. It is established that thisequation is closely connected with the problem of searching for invariantsubspaces of the Hamiltonian  $ {\bf H}=\left[ \begin{array}{lr} A & B B^{*} & A' \end{array}\right]. $  The orthogonality and expansion theorems are proved for eigenfunction systemsof the Hamiltonian $ H=A + W $. Scattering theory is developed for thisHamiltonian in the case where the operator $A$ has continuous spectrum.Comment: 20 pages, 94 kB, RevTeX; Published version of the pape

Removal of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian