Generalized difference spaces of non-absolute type of convergent and null sequences
type: Item
instance of: scholarly article
title: Generalized difference spaces of non-absolute type of convergent and null sequences
zbMATH Open document ID: 1267.46017
DOI: 10.1155/2012/435076
author: Abdulcabbar Sönmez
author: Feyzi Başar
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: The aim of the present paper is to introduce the spaces \(c^\lambda_0(B)\) and \(c^\lambda(B)\) of generalized difference sequences. These spaces are \(BK\)-spaces of non-absolute type and norm isomorphic to the spaces \(c_0\) and \(c\), respectively. Furthermore, we derive some inclusion relations, determine the \(\alpha\)-, \(\beta\)-, and \(\gamma\)-duals of those spaces, and construct their Schauder bases. Finally, we characterize some matrix classes from the spaces \(c^\lambda_0(B)\), and \(c^\lambda(B)\) to the spaces \(\ell_p\), \(c_0\), and \(c\).
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A35
zbMATH DE Number: 6134090
zbMATH Keywords: difference sequence
zbMATH Keywords: \(BK\)-spaces
Wikidata QID: Q58695137
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/435076
OpenAlex ID: W1985517770
cites work: Q4692979
cites work: On the paranormed Riesz sequence spaces of non-absolute type
cites work: On Some Euler Sequence Spaces of Nonabsolute Type
cites work: On the Euler sequence spaces which include the spaces \(\ell_{p}\) and \(\ell_{\infty}\). I
cites work: On the new sequence spaces which include the spaces \(c_0\) and \(c\)
cites work: Some new paranormed sequence spaces.
cites work: Q5703654
cites work: Q4493038
cites work: Matrix transformations between sequence spaces of generalized weighted means.
cites work: Q4195411
cites work: Q3023739
cites work: Some new sequence spaces derived by the domain of the triple band matrix
cites work: Almost convergence and triple band matrix
cites work: Q3050957
cites work: On some new sequence spaces and related matrix transformations
cites work: Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness
cites work: Some new difference sequence spaces
cites work: Q4455973
cites work: On Certain Sequence Spaces
cites work: The dual spaces of sets of difference sequences of order \(m\) and matrix transformations
cites work: On some new difference sequence spaces of non-absolute type
cites work: Q2996646
cites work: Q3994336
cites work: Q3312652
cites work: Matrixtransformationen von Folgenräumen. Eine Ergebnisübersicht
cites work: Q4728824
cites work: The fine spectrum and the matrix domain of the difference operator \(\Delta\) on the sequence space \(l_{p},\;(0<p<1)\)
cites work: Matrix transformations between the sequence space BVP and certain BK spaces
description: scientific article; zbMATH DE number 6134090