  The helical magnetorotational instability is known to work for resistive
rotational flows with comparably steep negative or extremely steep positive
shear. The corresponding lower and upper Liu limits of the shear are
continuously connected when some axial electrical current is allowed to flow
through the rotating fluid. Using a local approximation we demonstrate that the
magnetohydrodynamic behavior of this dissipation-induced instability is
intimately connected with the nonmodal growth and the pseudospectrum of the
underlying purely hydrodynamic problem.
