  In some recent literature the role of non self-adjoint Hamiltonians, $H\neq
H^\dagger$, is often considered in connection with gain-loss systems. The
dynamics for these systems is, most of the times, given in terms of a
Schr\"odinger equation. In this paper we rather focus on the Heisenberg-like
picture of quantum mechanics, stressing the (few) similarities and the (many)
differences with respected to the standard Heisenberg picture for systems
driven by self-adjoint Hamiltonians. In particular, the role of the symmetries,
*-derivations and integrals of motion is discussed.
