$C$-groups and mixed $C$-groups of bounded linear operators on non-archimedean Banach spaces

Abstract

We introduce and study C-groups and mixed C-groups of bounded linear operators on non-archimedean Banach spaces. Our main result extends some existing theorems on this topic. In contrast with the classical setting, the parameter of a given C-group (or mixed C-group) belongs to a clopen ball Ωr of the ground field K. As an illustration, we discuss the solvability of some homogeneous p-adic differential equations for C-groups and inhomogeneous p-adic differential equations for mixed C-groups when α = −1. Examples are given to support our work.