\(p\)-adic semi-Montel spaces and polar inductive limits (Q689876)

The paper is concerned with locally convex spaces over a complete non- archimedean valued field. A semi-Montel space \(E\) is a locally convex space satisfying: every bounded subset of \(E\) is compactoid. Nuclear spaces are compactoid, but not conversely. Indeed a nuclear space is polar and a semi-Montel space is in general not polar. The paper gives a characterization of semi-Montel spaces. Using this it is shown that a polar semi-Montel space is the inductive limit of nuclear spaces.