  In this article we use the homological methods of the theory of quasi-abelian
categories and some results from functional analysis to prove Theorems A and B
for (a broad sub-class of) dagger quasi-Stein spaces. In particular we show how
to deduce these theorems from the vanishing, under certain hypothesis, of the
higher derived functors of the projective limit functor. Our strategy of the
proof generalizes and puts in a more formal framework the Kiehl's proof for
rigid quasi-Stein spaces.
