Some B-difference sequence spaces derived by generalized means and compact operators

Abstract

Abstract. This paper presents new sequence spaces X(r, s, t, p; B) for X ∈ {l ∞ (p), c(p), c 0 (p), l(p)} defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the spaces X(r, s, t, p; B) for X ∈ {c(p), c 0 (p), l(p)} have Schauder basis. Furthermore, the α-, β-, γ-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from X(r, s, t, p; B) to X. Finally, some classes of compact operators on the space l p (r, s, t; B) are characterized by using the Hausdorff measure of noncompactness.