Generalized Köthe-Toeplitz duals, s-complete spaces and strongly-s-complete spaces in non-Archimedean analysis (Q2705017)

For a linear topological space \(X\) let \(\omega(X)\) denote the set of all sequences of elements of \(X\). The authors study the subspaces \(\varphi (x)\), \(c_0(x)\) and \(m(x)\) of \(w(x)\) where \(x\) is a non-archimedian Fréchet space, generalize the Köthe-Toeplitz duality for these spaces and characterize the duals of \(\varphi(x)\), \(c_0(x)\), \(m(x)\) and \(\omega(x)\). Topologizing \(\omega(x)\) in three different ways, they obtain three different versions of the property ``perfect'' and of the property ``complete'' of subsets of \(\omega(x)\).