On the summability of pairs of sequences in a nonarchimedean field
type: Item
instance of: scholarly article
title: On the summability of pairs of sequences in a nonarchimedean field
zbMATH Open document ID: 0952.40004
author: V. Kalarani
published in: The Journal of Analysis
publication date: 2001-01-14T00:00:00Z
review text: Let \(K\) be a complete non-trivially valued nonarchimedean field and let \(S\) denote the vector space of all sequences \(x= (x_n)\) with \(x_n\in K\) for all \(n\in\mathbb{N}\). A sequence \((A_k)\) of infinite matrices \(A_k= [a^{(k)}_{nj}]\) with entries from \(K\) defines a bilinear map \(A\) of \(D(A):= \{(x,y)\in S\times S\mid \sum_n \sum_j a^{(k)}_{nj}x_ny_j\) converges for every \(k\in\mathbb{N}\}\) into \(S\). The author obtains sufficient conditions on \((A_k)\) in order that (1) \(A:c\times c\to c\), and (2) \(A:\ell_\infty\times c\to c\), where \(c\) and \(\ell_\infty\) are, respectively, the space of all convergent and all bounded sequences.
Mathematics Subject Classification ID: 40J05
zbMATH DE Number: 1417952
zbMATH Keywords: summability of pairs of sequences
zbMATH Keywords: nonarchimedean field
reviewed by: Toivo Leiger
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1417952