Topological duals of some paranormed sequence spaces
type: Item
instance of: scholarly article
title: Topological duals of some paranormed sequence spaces
zbMATH Open document ID: 1035.46002
DOI: 10.1155/S0161171203210590
author: Nandita Rath
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50711
review text: Summary: Let \(P=(p_{k})\) be a bounded positive sequence and let \(A=(a_{nk})\) be an infinite matrix with all \(a_{nk}\geq 0\). For normed spaces \(E\) and \(E_{k}\), the matrix \(A\) generates the paranormed sequence spaces \([A,P]_{\infty}((E_{k}))\), \([A,P]_{0}((E_{k}))\), and \([A,P]((E))\), which generalise almost all the well-known sequence spaces such as \(c_{0}\), \(c\), \(l_{p}\), \(l_{\infty}\), and \(w_{p}\). In this paper, topological duals of these paranormed sequence spaces are constructed and general representation formulae for their bounded linear functionals are obtained in some special cases of the matrix \(A\).
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 40C05
Mathematics Subject Classification ID: 40H05
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 2012525
zbMATH Keywords: paranormed sequence spaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2012525