WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Some More Results on Matrix Transform between speed-Maddox
Spaces over Ultrametric Fields
Authors: ,
Abstract: Let K be a complete, non-trivially valued, ultrametric (or nonarchimedean) field, and $$λ= \left\{ λ_{κ}\right\}$$ -a sequence in K with the property $$0 < | λ_{n}|\nearrow$$ $$∞, n\rightarrow ∞,$$ i.e., the speed of convergence. In the present paper, in the ultrametric field K, convergence with speed and boundedness with speed are studied. First, the concepts of Maddox space and speed-Maddox space, paranormed λ-zero-convergence, paranormed λ-convergence, paranormed absolute λ-convergence and paranormed λ-boundedness over K have been introduced. Necessary and sufficient conditions are found for a matrix A over K to transform the set of all paranormally absolute λ- convergent sequences into the set of all paranormally absolute μ-convergent, all paranormally μ-zeroconvergent, all paranormally μ-convergent or all paranormally μ-bounded sequences, where μ is another speed in K. Two examples are given as applications, where A is the Srinivasan's method Y.
Search Articles
Keywords: Ultrametric (or nonarchimedean) field, matrix transforms, speed-Maddox spaces, paranormed
boundedness with speed, paranormed convergence with speed, paranormed zero-convergence
with speed, paranormed absolute convergence with speed
Pages: 542-550
DOI: 10.37394/23206.2025.24.54