ON BOUNDEDNESS WITH SPEED λ IN ULTRAMETRIC FIELDS

In 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, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K