On Some New Generalized Difference Sequence Spaces of Nonabsolute Type

Abstract

We define a new triangle matrix W^=(wnkλ) by the composition of the matrices Λ=(λnk) and B(r,s,t). Also, we introduce the sequence spaces c0λ(B^),cλ(B^),l∞λ(B^), and lpλ(B^) by using matrix domain of the matrix W^ on the classical sequence spaces c0,c,l∞, and lp, respectively, where 1≤p<∞. Moreover, we show that the space μλ(B^) is norm isomorphic to μ for μ∈{c0,c,l∞,lp}. Furthermore, we establish some inclusion relations concerning those spaces and determine α-, β-, and γ-duals of those spaces and construct the Schauder bases c0λ(B^),cλ(B^), and lpλ(B^). Finally, we characterize the classes (μ1λ(B^):μ2) of infinite matrices where μ1∈{c,c0,lp} and μ2∈{l∞,c,c0,lp}.