MATRIX TRANSFORMS FROM THE SET OF SEQUENCES BOUNDED WITH SPEED INTO THE SPEED-MADDOX SPACES OVER ULTRAMETRIC FIELDS

Abstract

Let K be a complete, non-trivially valued, ultrametric (or non-archimedean) field, and λ = {λ_n} - a sequence in K with the property 0 < |λ_n| ↗ ∞, n → ∞, i.e., the speed of convergence. In the present paper, the concepts of boundedness and convergence with speed and speed-Maddox spaces over K, where the
speed is defined by λ, have been recalled. Let μ be another speed in K. Necessary and sufficient conditions are found for a matrix A over K to transform all λ-bounded sequences over K into speed-Maddox spaces over K, where the speed is defined by μ.