On Some Difference Sequence Spaces of Weighted Means and Compact Operators?

Abstract

In the peresent paper, by using generalized weighted mean and difference matrix of order m, we introduce the sequence spaces X(u, v, Delta((m))), where X is one of the spaces l(infinity), c or c(0). Also, we determine the alpha-, beta- and gamma-duals of those spaces and construct their Schauder bases for X is an element of {c, c(0)}. Morever, we give the characterization of the matrix mappings on the spaces X(u, v, Delta(m)) for X is an element of {l(infinity), c, c(0)}. Finally, we characterize some classes of compact operators on the spaces l(1) (u, v, Delta(m)) and c(0)(u, v, Delta(m)) by using the Hausdorff measure of noncompactness.