Abstract. In this article we characterize invertible operators on a complete topological vector space generalizing the classical concept on invertibility of operators on normed linear spaces and Hilbert spaces. This characterization is employed to characterize invertible composition operators on the weighted locally convex spaces of continuous functions and the weighted spaces of cross-sections. Some examples are presented to give an insight into the theory.

AMS Subject Classification (1991): 47B38, 47A05, 46E10, 46E40

Received June 21, 1994. (Registered under 5601/2009.)