# Statistical convergence in non-archimedean Köthe sequence spaces

Volume 23, Issue 2, pp 80--85
Publication Date: October 09, 2020 Submission Date: July 22, 2020 Revision Date: August 04, 2020 Accteptance Date: August 17, 2020
• 77 Views

### Authors

D. Eunice Jemima - Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur , Chennai-603203, India. V. Srinivasan - (Retd. Professor) Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur , Chennai-603203, India.

### Abstract

The aim of this paper is to examine statistical convergence in a Köthe sequence space, when the sequences have their entries in a non-archimedean field $\mathscr{K}$ which is both non-trivial and complete under the metric induced by the valuation $|\ .\ |:\mathscr{K}\to \left[0,\infty \right)$, which is denoted by $\textit{K(B)}$.

### Share and Cite

##### ISRP Style

D. Eunice Jemima, V. Srinivasan, Statistical convergence in non-archimedean Köthe sequence spaces, Journal of Mathematics and Computer Science, 23 (2021), no. 2, 80--85

##### AMA Style

Jemima D. Eunice, Srinivasan V., Statistical convergence in non-archimedean Köthe sequence spaces. J Math Comput SCI-JM. (2021); 23(2):80--85

##### Chicago/Turabian Style

Jemima, D. Eunice, Srinivasan, V.. "Statistical convergence in non-archimedean Köthe sequence spaces." Journal of Mathematics and Computer Science, 23, no. 2 (2021): 80--85

### Keywords

• Köthe space
• non-archimedean field
• non-archimedean Köthe space
• statistical convergence

•  40A35
•  46E30
•  46S10

### References

• [1] G. Bachman, Introduction to $p$-Adic Numbers and Valuation Theory, Academic Press, New York-London (1964)

• [2] H. Çakallı, A Study on statistical convergence, Funct. Anal. Approx. Comput., 1 (2009), 19--24

• [3] N. De Grande-De Kimpe, Non-archimedean nuclearity, Study group on ultrametric analysis (Inst. Henri Poincare), 3 (1982), 8 pages

• [4] H. Fast, Sur la convergence statistique, (French) Colloq. Math., 2 (1951), 241--244

• [5] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301--314

• [6] J. A. Fridy, H. I. Miller, A matrix characterization of statistical convergence, Analysis, 11 (1991), 59--66

• [7] G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, Oxford (1949)

• [8] A. F. Monna, Sur le theoreme de Banach-Steinhaus, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag. Math., 25 (1963), 121--131

• [9] L. Narici, E. Beckenstein, G. Bachman, Functional Analysis and Valuation Theory, Marcel Dekker, New York (1971)

• [10] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139--150

• [11] W. Śliwa, Every non-normable non-archimedean Köthe space has a quotient without the bounded approximation property, Indag. Mathem. (N.S.), 15 (2004), 579--587

• [12] K. Suja, V. Srinivasan, On statistically convergent and statistically cauchy sequences in non-archimedean fields, J. Adv. Math., 6 (2014), 1038--1043

• [13] J. Uma, V. Srinivasan, Statistical convergence in generalized difference sequence spaces over non-archimedean fields, Int. J. Pure Appl. Math., 113 (2017), 280--289