On the space of bounded Euler difference sequences and some classes of compact operators

In this paper we consider the new one sequence space a(infinity)(r)(Delta) and characterize matrix transformations between a(infinity)(r)(Delta) and certain BK spaces. Further, we define the subclasses of compact operators applying the Hausdorff measure of noncompactness. Our results extend those in [C. Aydin, F. Basar, Some new difference sequence spaces, Appl. Math. Comput. 157 (2004) 677-693; I. Djolovic, Compact operators on the spaces a(0)(r)(Delta) and a(c)(r)(Delta), J. Math. Anal. Appl. 318 (2006) 658666]. (c) 2006 Elsevier Inc. All rights reserved.