The study reveals necessary conditions for matrix transforms to convert bounded sequences into speed-Maddox spaces, highlighting ultrametric properties.
Let K be a complete, non-trivially valued, ultrametric (or non-archimedean) field, and ? = {n?}-a sequence in K with the property 0 < |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 ?, have been recalled. Let ? be another speed in K. Necessary and sufficient conditions are found for a matrix A over K to transform all ?-bounded sequences over K into speed-Maddox spaces over K, where the speed is defined by ?.
No takes yet. Share an insight, caveat, or question.
Natarajan et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: