On convergence and summability with speed in ultrametric fields

Abstract

Throughout the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K . Following Kangro [2–4], we introduce the concepts of convergence with speed λ (or λ -convergence) and λ -summability by the infinite matrix A (or A λ summability) in K . We then prove a characterization of the matrix class ( c λ ,c µ ), where c λ denotes the set of all λ -convergent sequences.