Closed graph and open mapping theorems for topological -modules and applications

الأصل · EN

We present closed graph and open mapping theorems for -linear maps acting between suitable classes of topological and locally convex topological -modules. This is done by adaptation of De Wilde's theory of webbed spaces and Adasch's theory of barrelled spaces to the context of locally convex and topological -modules respectively. We give applications of the previous theorems to Colombeau theory as well to the theory of Banach -modules. In particular we obtain a necessary condition for -hypoellipticity on the symbol of a partial differential operator with generalized constant coefficients.