On compact operators and some Euler [formula omitted]-difference sequence spaces

Abstract

Altay and Başar (2005) [1] and Altay, Başar and Mursaleen (2006) [2] introduced the Euler sequence spaces e 0 t , e c t and e ∞ t . 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 e 0 t ( B ( m ) ) , e c t ( B ( m ) ) and e ∞ t ( B ( m ) ) consisting of all sequences whose B ( m ) -transforms are in the Euler spaces e 0 t , e c t and e ∞ t , respectively. Moreover, we determine the α-, β- and γ-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 ∞ t ( B ( m ) ) .