P-Adic Semi-Montel Spaces and Polar Inductive Limits

In this paper we give a characterization of p-adic semi-Montel spaces which allows us to describe the finest polar semi-Montel topology coarser than the original topology of a locally convex space. As an application we derive that every polar semi-Montel space is a polar inductive limit of a family of nuclear spaces. We also pay attention to the connection with compactifying operators.