The fine spectrum and the matrix domain of the difference operator \(\Delta\) on the sequence space \(l_{p},\;(0<p<1)\)
type: Item
instance of: scholarly article
title: The fine spectrum and the matrix domain of the difference operator \(\Delta\) on the sequence space \(l_{p},\;(0<p<1)\)
zbMATH Open document ID: 1173.47021
published in: Communications in Mathematical Analysis
publication date: 2009-04-24T00:00:00Z
review text: The authors study the fine spectrum and the matrix domain \(bv_{p}\), \(0<p<1\), of the difference operator \(\Delta\) in the sequence space \(\ell_{p}\). They prove that \(bv_{p}\) is a \(p\)-normed space and is linearly isomorphic to the space \(\ell _{p}\). Finally, the \(\beta\)- and \(\gamma\)-duals of the space \(bv_{p}\) are computed and the characterization of the matrix mappings from the space \(bv_{p}\) into \(\mu\) and from \(\mu\) into \(bv_{p}\) is given, where \(\mu\) is any given sequence space.
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 40J05
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 5547345
zbMATH Keywords: spectrum of a linear operator
zbMATH Keywords: difference sequences
zbMATH Keywords: matrix mappings
author: Bilal Altay
author: Feyzi Başar
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5547345