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∞r(▵) and characterize matrix transformations between a∞r(▵) 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. Başar, Some new difference sequence spaces, Appl. Math. Comput. 157 (2004) 677–693; I. Djolović, Compact operators on the spaces a0r(▵) and acr(▵), J. Math. Anal. Appl. 318 (2006) 658–666].