A set of new paranormed difference sequence spaces and their matrix transformations

摘要

In this paper, by using a new difference operator Δ_j, the author likes to introduce new classes of paranormed difference sequence spaces X(Δ_j, u, v; p) for X ε ?_∞, c, c _0 and investigates their topological structures, where (u _n) and (v_n) are two sequences satisfying certain conditions. The difference operator Δ_j is defined by Δ_j(x_j) = jx_j - (j + 1)x_(j+1) for all j ε N, the set of positive integers. Also, we determine the α-, β- and γ-duals of these classes. Furthermore, the matrix transformations from these classes to the sequence spaces l_∞(q), c_0(q) and c(q) have been characterized.