On the weighted function space [formula omitted] in the non-Archimedean setting

Abstract

For V a Nachbin family, on a zero-dimensional Hausdorff topological space X, and E a non-Archimedean Hausdorff locally convex space, it is shown that the dual spaces of the Nachbin spaces CVo(X) and CVo(X,E) are algebraically isomorphic to certain spaces of measures on a ring of subsets of X. Also, the space of all continuous linear maps, from CVo(X,E) to another locally convex space F, is algebraically isomorphic to a space of L(E,F)-valued measures.