On \(p\)-adic locally convex spaces (Q2751732)

The purpose of this paper is to give some results for non-Archimedean locally convex spaces. Let \(E\) and \(F\) be locally convex spaces. In Section 2, the results are mainly concerned with topological isomorphism and compactoidness when \(E\), \(F\) are either both Fréchet polar spaces or both \((dF)\)-spaces. The intent of Section 3 is to look for the finest locally convex topology on \(E\) which coincides with the weak topology on bounded subsets of \(E\). The next section presents an analogue of the classical Schauder theorem [see the work of \textit{H. Jarchow}, ``Locally convex spaces'', Stuttgart (1981; Zbl 0466.46001)]. Dual properties of \(E\) are discussed in Sections 5 and 6. For various terminologies, one may refer to \textit{W. H. Schikhof} [Bull. Soc. Math. Belg., Sér. B 38, 187-207 (1986; Zbl 0615.46071)].NEWLINENEWLINEFor the entire collection see [Zbl 0969.00058].