Sequence of Linear Operators in Non-Archimedean Banach Spaces

Abstract

The aim of this paper is to find a non-Archimedean counterpart of the generalized convergence of closable unbounded linear operators as defined by Kato (Perturbation Theory for Linear Operators, 2nd edn. In: Grundlehren der Mathematischen Wissenschaften, Band 132, Springer, Berlin, 1976). Moreover, we prove that this convergence can be considered as a generalization of convergence in norm for unbounded linear operators on non-Archimedean Banach spaces (see Theorem 3.8).