  Effective (i.e., subspace-constrained) Hamiltonians become, by construction,
energy-dependent while all the energy-dependent forces prove non-linear because
the energy itself is merely an eigenvalue of the Hamiltonian H. One of the most
natural resolutions of such a puzzle is proposed via an introduction of teh two
separate linear representatives of the respective right and left action of
H=H(E). Both the new energy-independent operators are non-Hermitian so that the
formalism admits a natural extension to non-Hermitian initial H(E)s.
