Closed graph and open mapping theorems for topological \wt\C-modules and applications

2006/08/03 by Claudia Garetto, Garetto, Claudia
Computer Science · Mathematics · #13J99 #46A30 #46F30 #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.math/0608087

openalex publication_date 2006/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present closed graph and open mapping theorems for \wt\C-linear maps acting between suitable classes of topological and locally convex topological \wt\C-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 \wt\C-modules respectively. We give applications of the previous theorems to Colombeau theory as well to the theory of Banach \wt\C-modules. In particular we obtain a necessary condition for \Ginf-hypoellipticity on the symbol of a partial differential operator with generalized constant coefficients.

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