  Spaces of homogeneous polynomials on a Banach space are frequently equipped
with quasinorms instead of norms. In this paper we develop a technique to
replace the original quasi-norm by a norm in a dual preserving way, in the
sense that the dual of the space with the new norm coincides with the dual of
the space with the original quasi-norm. Applications to problems on the
existence and approximation of solutions of convolution equations and on
hypercyclic convolution operators on spaces of entire functions are provided.
