Let K be a complete, non-trivially valued, ultrametric (or non-archimedean) field. We recall the notions of boundedness and convergence with speed and speed-Maddox spaces over K, where the speed is defined by a sequence = \ₙ\ in K with the property 0 < |ₙ|, n, and define a new notion of absolute convergence with speed over K. Let be another speed in K. The necessary and sufficient conditions for a matrix A over K would transform all sequences that are -convergent or absolutely -convergent over K into the speed-Maddox spaces over K, where the speed is defined by.
Natarajan et al. (Wed,) studied this question.
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