Malkowsky, E.; Parashar, S. D. Matrix transformations in spaces of bounded and convergent difference sequences of order \(m\). (English) Zbl 0872.40002 Analysis 17, No. 1, 87-97 (1997). Summary: Let \(m\) be a positive integer. We define the sets \(c_0(\Delta^{(m)})\), \(c(\Delta^{(m)})\) and \(l_\infty(\Delta^{(m)})\) of sequences the \(m\)th order differences of which are convergent to zero, convergent or bounded, give Schauder bases for \(c_0(\Delta^{(m)})\) and \(c(\Delta^{(m)})\), and compute the \(\alpha\)- and \(\beta\)-duals of \(c_0(\Delta^{(m)})\), \(c(\Delta^{(m)})\) and \(l_\infty(\Delta^{(m)})\). Finally we characterize matrix transformations between these spaces. For \(m=1\), some of our results yield those in H. Kizmaz [Can. Math. Bull. 24, No. 2, 169-176 (1981; Zbl 0454.46010)]. Cited in 1 ReviewCited in 36 Documents MSC: 40H05 Functional analytic methods in summability 46A45 Sequence spaces (including Köthe sequence spaces) Keywords:convergent difference sequences; Banach space; differences; Schauder bases; matrix transformations Citations:Zbl 0454.46010 PDFBibTeX XMLCite \textit{E. Malkowsky} and \textit{S. D. Parashar}, Analysis 17, No. 1, 87--97 (1997; Zbl 0872.40002) Full Text: DOI