$C$-groups and mixed $C$-groups of bounded linear operators on non-archimedean Banach spaces
DOI:
https://doi.org/10.33044/revuma.2074Abstract
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 $\Omega_{r}$ of the ground field $\mathbb{K}$. 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 $\alpha=-1$. Examples are given to support our work.
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Copyright (c) 2022 Abdelkhalek El Amrani, Aziz Blali, Jawad Ettayb

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