Fredholm theory for \(p\)-adic locally convex spaces (Q1191389)

Let \(K\) be a non-Archimedean non-trivially valued complete field with a valuation. Let \(E\) be a locally \(K\)-convex space. For a subset \(A\) of \(E\), \([A]\) denotes the linear span of \(A\). \(E_ A\) denotes \([A]\) normed by the Minkowski functional \(p_ A\) when \(A\) is absolutely convex and bounded. \(A\) is said to be completing if \(E_ A\) is complete. A linear map \(T: E\to F\), \(E\), \(F\) locally \(K\)-convex spaces over \(K\) is said to be semi-compact if there exists a compactoid, completing set \(D\) of \(F\) such that the inverse image of \(D\) under \(T\) is a neighbourhood of 0 in \(E\). The authors study the space of semi-compact operators leading to the Fredholm theory for such operators. In the case \(E\), \(F\) are Banach spaces over \(K\), what the authors have obtained agrees with that obtained by \textit{W. H. Schikhof} [On \(p\)-adic compact operators, Report 8911, Dept. of Mathematics, Catholic University, Nijmegen (1989)].