On some sequence spaces defined by a modulus
type: Item
instance of: scholarly article
title: On some sequence spaces defined by a modulus
zbMATH Open document ID: 0935.46005
author: V. K. Bhardwaj
author: Niranjan Singh
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2000-05-10T00:00:00Z
review text: There are ten results in this paper. The following result typifies the standard of the results: For any nonnegative regular matrix \(A= (a_{nk})\) and moduli \(f\) and \(g\), \[ w_\infty(A, g)\subset w_\infty(A, f)\Leftrightarrow \limsup_{x\to\infty} {f(x)\over g(x)}< \infty, \] where \[ w_\infty(A, f)= \Biggl\{(x_k): \sup_n \sum^\infty_{k=1} a_{nk} f(|x_k|)< \infty\Biggr\}. \] Information on multipliers for \(w_\infty(A, f)\) is also given. There is a result on conditions under which \(w_\infty(A,f)= s\), the space of all complex sequences.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 1359898
zbMATH Keywords: sequence spaces
zbMATH Keywords: Cesàro summability
zbMATH Keywords: nonnegative regular matrix
zbMATH Keywords: moduli
zbMATH Keywords: multipliers
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1359898