On Some New Generalized Difference Sequence Spaces of Nonabsolute Type

Abstract

We define a new triangle matrixW^=(wnkλ)by the composition of the matricesΛ=(λnk)andB(r,s,t). Also, we introduce the sequence spacesc0λ(B^),cλ(B^),l∞λ(B^), andlpλ(B^)by using matrix domain of the matrixW^on the classical sequence spacesc0,c,l∞, andlp, respectively, where1≤p<∞. Moreover, we show that the spaceμλ(B^)is norm isomorphic toμforμ∈{c0,c,l∞,lp}. Furthermore, we establish some inclusion relations concerning those spaces and determineα-,β-, andγ-duals of those spaces and construct the Schauder basesc0λ(B^),cλ(B^), andlpλ(B^). Finally, we characterize the classes(μ1λ(B^):μ2)of infinite matrices whereμ1∈{c,c0,lp}andμ2∈{l∞,c,c0,lp}.