  We answer in the affirmative the surprisingly difficult questions: If a
complex Banach space possesses a real predual X, then is X a complex Banach
space?
  If a complex Banach space possesses a real predual, then does it have a
complex predual? We also answer the analogous questions for operator spaces,
that is spaces of operators on a Hilbert space, up to complete isometry. Indeed
we use operator space methods to solve the Banach space question above.
