REPRESENTATION THEOREMS OF LINEAR OPERATORS ON P-ADIC FUNCTION SPACES

Let X be a 0-dimensional Hausforff topological space, E, F non-archimedean Banach spaces and Cb(X,E) the space of all continuous E-valued functions on X provided with two strict topologies. In this paper we show that every F−valued linear operator which is strictly continuous can be represented by a certain L(E,F)−valued measure defined on the ring of all clopen subsets of X. ∗This work is partially supported by Fondecyt No. 1020288 98 Jose ́ Aguayo, Elsa Chandía and Jacqueline Ojeda 1. Introduction an