Schauder decompositions and functional calculus

We establish a functional calculus, with nice properties, for one and several continuous operators on some non-normable locally convex spaces, more specifically, for operators on the space H(Cν) of entire functions and on other power series spaces. In particular we obtain spectral mapping theorems. The calculus rests on Schauder decompositions for the spaces under consideration, which are of independent interest.