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

Authors

  • Abdelkhalek El Amrani Department of mathematics and computer science, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Atlas F`es, Morocco
  • Aziz Blali Ecole Normale Sup´erieure, Department of mathematics, Sidi Mohamed Ben Abdellah University, Bensouda-F`es, Morocco
  • Jawad Ettayb Department of mathematics and computer science, Sidi Mohamed Ben Abdellah University, Faculty of Sciences Dhar El Mahraz, Atlas F`es, Morocco

DOI:

https://doi.org/10.33044/revuma.2074

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 $\Omega_{r}$ 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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References

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Published

2022-05-30

Issue

Vol. 63 No. 1 (2022)

Section

Article

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Copyright (c) 2022 Abdelkhalek El Amrani, Aziz Blali, Jawad Ettayb

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