Journal article

Publication year: 2008

Pages: 700-714

Journal: Applied Mathematics and Computation

Volume number: 198

Issue number: 2

ISSN: 0096-3003

eISSN: 1873-5649

DOI Link: https://doi.org/10.1016/j.amc.2007.09.008

Publisher: Elsevier

Abstract: 
We de. ne some new sets of sequences the mth-order differences of which are alpha-bounded, convergent and convergent to zero, and apply the general methods in [ E. Malkowsky, V. Rakocevic , On matrix domains of triangles, Appl. Math. Comput. 189 ( 2) ( 2007) 1146 - 1163] to give Schauder bases for the latter two, determine their beta-duals and characterize matrix transformations on them. Our results generalize those in [ B. de Malafosse, The Banach algebra S-alpha and applications, Acta Sci. Math. ( Szeged) 70 ( 1 - 2) ( 2004) 125 - 145] and improve those in [ E. Malkowsky, S. D. Parashar, Matrix transformations in spaces of bounded and convergent difference sequences of order m, Analysis 17 ( 1997) 87 - 97]. We also establish identities and estimates for the Hausdorff measure of non-compactness of matrix operators from our spaces into the spaces of bounded, convergent and null sequences, and characterize the respective classes of compact operators. Some of these results generalize those in [ E. Malkowsky, V. Rakocevic , The measure of non-compactness of linear operators between spaces of mth-order difference sequences, Stud. Sci. Math. Hungar. 33 ( 1999) 381 - 391]. (C) 2007 Elsevier Inc. All rights reserved.

Harvard Citation style: Djolovic, I. and Malkowsky, E. (2008) Matrix transformations and compact operators on some new mth-order difference sequences, Applied Mathematics and Computation, 198(2), pp. 700-714. https://doi.org/10.1016/j.amc.2007.09.008

APA Citation style: Djolovic, I., & Malkowsky, E. (2008). Matrix transformations and compact operators on some new mth-order difference sequences. Applied Mathematics and Computation. 198(2), 700-714. https://doi.org/10.1016/j.amc.2007.09.008