On B~(m)-difference sequence spaces using generalized means and compact operators

摘要

In this paper, sequence spaces X(r, s, t; B~(m)) for X ∈ {l_∞, c, c_0} are introduced by combining the generalized means and the m-th order generalized difference operator B~(m)(u, v). It is shown that these spaces are complete normed linear spaces and the spaces c_0(r, s, t; B~(m)), c(r, s, t; B~(m)) have Schauder bases. Furthermore, the α-, β-, γ-duals of these spaces are computed. The necessary and sufficient conditions for some matrix transformations from X(r, s, t; B~(m)) to Y, where X, Y ∈ {l_∞,c,c_0}, are also obtained. Finally, some classes of compact operators on the spaces X(r, s, t; B~(m)) for X ∈ {l_∞, c,c_0} are characterized by using the Hausdorff measure of noncompactness.