Some B-difference sequence spaces derived by generalized means and compact operators
Kragujevac Journal of Mathematics
This paper presents new sequence spaces X(r, s, t, p; B) for X ∈ (l∞(p), c(p), c0(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), c0(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 lp(r, s, t; B) are characterized by using the Hausdorffmeasure of noncompactness.
Maji, A.; Manna, A.; and Srivastava, P. D., "Some B-difference sequence spaces derived by generalized means and compact operators" (2017). Journal Articles. 2771.