\(C_{0}\)-semigroups of linear operators on some ultrametric Banach spaces
The author describes non-Archimedean analogs of the basic notions of the theory of semigroups of linear operators on Banach spaces. The results given are quite easy and similar to the classical case, such as the generation of a semigroup by a bounded operator of a small norm, or a link from semigroups to abstract Cauchy problems. The converse link, which requires a uniqueness result, is not considered. For the nontrivial aspects of non-Archimedean abstract Cauchy problems, the reader may want to consult \textit{M. L. Gorbachuk} and \textit{V. I. Gorbachuk} [Methods Funct. Anal. Topol. 9, No. 3, 207--212 (2003; Zbl 1037.47052); Proceedings of the Steklov Institute of Mathematics 245, 91--97 (2004; Zbl 1105.34320)].
scientific article; zbMATH DE number 5164017