INTERSECTIONS OF FRECHET-SCHWARTZ-SPACES AND THEIR DUALS

In this article the structure of the intersections of a Frechet Schwar tz space F and a (DFS)-space E = ind(n)E(n) is investigated. A complet e characterization of the locally convex properties of E boolean AND F is given. This space is bornological if and only if the inductive lim it E + F is complete. The results are based on recent progress on the structure of (LF)-spaces. The article includes examples of (FS)-spaces F and (DFS)-spaces E such that there are sequentially continuous line ar forms on E boolean AND F which are not continuous, thus answering a question of Langenbruch.