Infinite matrices and almost convergent sequences
type: Item
instance of: scholarly article
title: Infinite matrices and almost convergent sequences
zbMATH Open document ID: 0843.46003
published in: Southeast Asian Bulletin of Mathematics
publication date: 1996-03-07T00:00:00Z
review text: Let \((p_k)\) be a sequence of real numbers with \(p_k> 0\). A sequence, whose \(k\)th term is \(x_k\), will be denoted by \(x\) or \((x_k)\). Let \[ \ell(p, s)= \Biggl\{x: \sum_k k^{-s} |x_k|^{p_k}< \infty,\;s\geq 0\Biggr\}. \] Let \(f\) be the space of all almost convergent sequences. Let \(f_\infty\) be the space of all \(f\)-bounded sequences. In this paper, the class \((\ell(p, s), f)\) of all infinite matrices transforming \(\ell(p, s)\) into \(f\), and the class \((\ell(p, s), f_\infty)\) of all infinite matrices transforming \(\ell(p, s)\) into \(f_\infty\) are characterized.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 853036
zbMATH Keywords: space of all almost convergent sequences
zbMATH Keywords: infinite matrices
author: M. Mursaleen
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 853036