The main goal of this paper is to construct the state diagram for closed linear operators \(A: D(A) \subset X \to Y\) with dense domain \(D(A)\), where \(X,Y\) are non-archimedean Banach spaces over a complete non-archimedean and non-trivially valued field \(K\). The case of continuous operators \(A\) was studied by \textit{R. L. Ellis} [J. Reine Angew. Math. 229, 155--162 (1968; Zbl 0161.34402) and \textit{V. M. Onieva} [Rev. Mat. Hisp.--Am. (4) 28, 188--195 (1968; Zbl 0169.16602)] when \(D(A) =X\) and \(K\) is spherically complete and by \textit{J. Martínez--Maurica} [``Diagramas de estados de operadores entre espacios normados no arquimedianos'' (Thesis, Universidad de Bilbao) (1977)] for any \(K\) and when \(\overline{D(A)} = X\). Hence the present paper completes these previous contributions about \(p\)-adic state diagrams. The authors start by showing several properties of closed linear operators \(A\) with dense domain, centering the attention on those concerning relations between kernels and ranges of \(A\) and its adjoint \(A'\). Most of the statements and proofs are inspired by their classical analogues, but sometimes they require some changes to be adapted to the non-archimedean context. The authors then apply their results to obtain a \(p\)-adic closed range theorem for this kind of operators \(A\), which establishes that if \(X\) and \(Y\) satisfy certain Hahn-Banach properties, then the range of \(A\) is (weakly) closed if and only if the range of \(A'\) is (weakly\(^{*}\)) closed. This is an extension of the corresponding theorem proved by the reviewer for continuous linear operators \(X \to Y\) in [\textit{C. Pérez-García}, Bull. Belg. Math. Soc. -- Simon Stevin 2002, Suppl., 149--157 (2002; Zbl 1080.47053)]. The authors only give the theorem for densely valued fields \(K\). The reason of this restriction is not clear to me. It seems that it is because in the statements of some results (Theorem 2.6 and Corollary 2.9), which are needed to get this closed range theorem, it is assumed that the valuation of \(K\) is dense. But in their proofs, the authors just say that it is possible to argue as in the paper of the reviewer mentioned above, where no assumption about density of the valuation is required. So I think that there is some hope for the validity, for discretely valued fields (which are spherically complete), of the closed range theorem given in the present paper. It would be interesting to investigate this question. The theory developed in the paper leads finally to the state diagram for closed linear operators with dense domain. There are some states that, according to that theory, are not impossible. It would be nice to give examples showing that indeed they are possible. The diagram constructed in the paper (for densely valued fields) is a really non-archimedean one in the sense that differs from its classical counterpart. In fact, some states that are possible for real or complex Banach spaces, cannot occur in the \(p\)-adic setting, under some forms of the Hahn--Banach theorem, which for instance work for spherically complete \(K\).