On some new sequence spaces of invariant means
type: Item
instance of: scholarly article
title: On some new sequence spaces of invariant means
zbMATH Open document ID: 0909.46004
DOI: 10.1023/A:1006547204898
author: M. Mursaleen
author: A. K. Gaur
author: Tariq A. Chishti
published in: Acta Mathematica Hungarica
publication date: 1998-11-23T00:00:00Z
review text: Generalizing previous work of \textit{G. Das} and \textit{S. K. Sahoo} [J. Math. Anal. Appl. 164, No. 2, 381-398 (1992; Zbl 0778.46011)] on the spaces \(w\), \([w]\) and \([w_1]\) of almost convergent sequences, the authors define new sequence spaces \(w_\sigma\), \([w]_\sigma\) and \([w_\sigma]\), replacing the translation mapping \(n\to n+1\) by a mapping \(\sigma\) of \(\mathbb N\) into itself and the Banach limit on \(\ell_\infty\) by a \(\sigma\)-invariant mean. Among other things, they show that a certain sublinear functional ``both dominates and generates \(\sigma\)-means'', and they derive some inclusion relations between the new sequence spaces. -- There are many (obvious) misprints.
reviewed by: Klaus Dieter Bierstedt
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46B45
zbMATH DE Number: 1226286
zbMATH Keywords: Banach limit
zbMATH Keywords: invariant mean
zbMATH Keywords: almost convergent sequences
zbMATH Keywords: inclusion relations
zbMATH Keywords: sublinear functional
MaRDI profile type: Publication
full work available at URL: a:1006547204898
OpenAlex ID: W1823225847
description: scientific article; zbMATH DE number 1226286