  Countable projective limits of countable inductive limits, called PLB-spaces,
of weighted Banach spaces of continuous functions have recently been
investigated by Agethen, Bierstedt and Bonet. We extend their investigation to
the case of holomorphic functions regarding the same type of questions, i.e. we
analyze locally convex properties in terms of the defining double sequence of
weights and study the interchangeability of projective and inductive limit.
