Geodesic
Matrix Transforms Into the Speed-Maddox Spaces Over Ultrametric Fields II
Publications de l'Institut Mathématique, _N_S_118 (2025) no. 132, p. 89

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DOI

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 $\mu=\{\mu_n\}$ in $K$ with the property $0|\mu_n|\nearrow\infty$, $n\to\infty$, and define new notion of absolute convergence with speed $\mu$ over $K$. Let $\lambda$ be another speed in $K$. The necessary and sufficient conditions for a matrix $A$ over $K$ would transform all sequences that are $\lambda$-convergent or absolutely $\lambda$-convergent over $K$ into the speed-Maddox spaces over $K$, where the speed is defined by $\mu$.
DOI : 10.2298/PIM2532089N
Classification : 40C05, 40D05, 40H05, 46S10
Keywords: ultrametric (or non-archimedean) field, matrix transforms, convergence with speed, boundedness with speed, absolute convergence with speed, speed-Maddox spaces 
Pinnangudi Narayanasubramanian Natarajan; Ants Aasma. Matrix Transforms Into the Speed-Maddox Spaces Over Ultrametric Fields II. Publications de l'Institut Mathématique, _N_S_118 (2025) no. 132, p. 89 . doi: 10.2298/PIM2532089N
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     journal = {Publications de l'Institut Math\'ematique},
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