J. Math. Computer Sci., 23 (2021), 80–85 Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs Statistical convergence in non-archimedean K ¨ othe sequence spaces D. Eunice Jemima a,∗ , V. Srinivasan b a Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, India. b (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 K¨ othe sequence space, when the sequences have their entries in a non-archimedean field K which is both non-trivial and complete under the metric induced by the valuation | . | : K → [0, ∞), which is denoted by K(B). Keywords: K¨ othe space, non-archimedean field, non-archimedean K ¨ othe space, statistical convergence. 2020 MSC: 40A35, 46E30, 46S10. c 2021 All rights reserved. 1. Introduction In classical analysis, the study of certain pairs of subspaces of the space of all real sequences was initiated by K¨ othe and Toeplitz, and a little later by K¨ othe alone. Lorentz and Wertheim, Dieudonne and Cooper generalized their concept. A set A of non-negative sequences (α n ) n∈N is called a K¨ othe set, if (i) for each n ∈ N, there exists α ∈ A with α n > 0; (ii) for each pair (α, β) ∈ A × A, there exists a γ ∈ A such that max(α n , β n )  γ n , for all n ∈ N. K¨ othe sequence spaces are defined classically as the orthogonals of certain subsets of K ¨ othe sets. They are locally convex topological vector spaces which are Hausdorff and complete. 1.1. Non-archimedean K¨ othe spaces Definition 1.1. Consider an infinite matrix B =(b n,k ) consisting of positive real numbers, and satisfying the condition b n,k  b n,k+1 , n, k = 1, 2, ··· . The non-archimedean K ¨ othe space K(B) associated with the matrix B is defined by De Grande-De Kimpe ∗ Corresponding author Email addresses: eunicejem@gmail.com (D. Eunice Jemima), drvsrinivas.5@gmail.com (V. Srinivasan) doi: 10.22436/jmcs.023.02.01 Received: 2020-07-22 Revised: 2020-08-04 Accepted: 2020-08-17