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

Altay and Basar (2005) [1] and Altay, Basar and Mursaleen (2006) [2] introduced the Euler sequence spaces e(0)(t), e(c)(t) and e(infinity)(t). Basarir and Kayikci (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 e(0)(t)(B-(m)), e(c)(t)(B-(m)) and e(infinity)(t)(B-(m)) consisting of all sequences whose B-(m)-transforms are in the Euler spaces e(0)(t), e(c)(t) and e(infinity)(t), respectively. Moreover, we determine the alpha-, beta- and gamma-duals of these spaces and construct the Schauder basis of the spaces e(0)(t)(B-(m)) and e(c)(t)(B-(m)). Finally, we characterize some matrix classes concerning the spaces e(0)(t)(B-(m)) and e(c)(t)(B-(m)) and give the characterization of some classes of compact operators on the sequence spaces e(0)(t)(B-(m)) and e(infinity)(t)(B-(m)). (C) 2011 Elsevier Inc. All rights reserved.