International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 52398, 9 pages

C0-semigroups of linear operators on some ultrametric Banach spaces

Toka Diagana

Department of Mathematics, Howard University, 2441 6th Street, NW Washington 20059, DC, USA

Received 20 August 2005; Revised 28 February 2006; Accepted 25 April 2006

Copyright © 2006 Toka Diagana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.