  We prove a technical result, showing that the existence of a closable
unbounded dual system in the sense of Voiculescu is equivalent to the
finiteness of free Fisher information. This approach allows one to give a
purely operator-algebraic proof of the computation of the non-microstates free
entropy dimension for generators of groups carried out in an earlier joint work
with I. Mineyev. The same technique also works for finite-dimensional algebras.
  We also show that Voiculescu's question of semi-continuity of free entropy
dimension, as stated, admits a counterexample. We state a modified version of
the question, which avoids the counterexample, but answering which in the
affirmative would still imply the non-isomorphism of free group factors.
