On some vector valued sequence spaces defined using a modulus function
type: Item
instance of: scholarly article
title: On some vector valued sequence spaces defined using a modulus function
zbMATH Open document ID: 0935.46008
author: P. D. Srivastava
author: Dalim K. Ghosh
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2000-05-04T00:00:00Z
review text: Let \(\{E_k\}\) be a sequence of complex Banach spaces with norms \(\|\cdot\|_{E_k}\) \((k=1,2,3,\dots)\) and \(F\) a normal sequence space with monotone paranorm \(g_F\) such that coordinatewise convergence implies convergence in paranorm and let \(f\) be a modulus function. Define \[ F(E_k, f)= \{(x_k): x_k\in E_k\;\forall k\text{ and }(f(\|x_k\|_{E_k}))\in F\}. \] The authors, among other results, prove the following theorem: \(F(E_k, f)\) is a complete paranormed space under the paranorm \(g(x)= g_F[(f(\|x_k\|_{E_k}))]\) for \(x= (x_k)\) belonging to \(F(E_k, f)\).
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A16
Mathematics Subject Classification ID: 46A80
Mathematics Subject Classification ID: 40H05
zbMATH DE Number: 1359899
zbMATH Keywords: vector valued sequence spaces
zbMATH Keywords: modulus function
zbMATH Keywords: monotone paranorm
zbMATH Keywords: coordinatewise convergence
zbMATH Keywords: convergence in paranorm
zbMATH Keywords: complete paranormed space
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1359899