On compact operators and some Euler B(m)-difference sequence spaces

Altay and Başar (2005) [1], and Altay, Başar and Mursaleen (2006) [2], introduced the Euler sequence spaces , and . Başarır and Kayıkçı (2009) [3] defined the B(m)-difference matrix and studied some topological and geometric properties of some generalized Riesz B(m)-difference sequence space. In this paper, we introduce the Euler B(m)-difference sequence spaces , and consisting of all sequences whose B(m)-transforms are in the Euler spaces , and , respectively. Moreover, we determine the α-, β- and γ-duals of these spaces and construct the Schauder basis of the spaces and . Finally, we characterize some matrix classes concerning the spaces and and give the characterization of some classes of compact operators on the sequence spaces and .