Seminormed spaces
The paper is concerned with the spectral analysis for the class of linear operators in non-archimedean Hilbert space, where is a diagonal operator and is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.
In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in...