Sequence spaces derived by the triple band generalized Fibonacci difference operator

Abstract

In this article we introduce the generalized Fibonacci difference operator F(B) by the composition of a Fibonacci band matrix F and a triple band matrix B(x, y, z) and study the spaces ℓk(F(B)) and ℓ∞(F(B)). We exhibit certain topological properties, construct a Schauder basis and determine the Köthe–Toeplitz duals of the new spaces. Furthermore, we characterize certain classes of matrix mappings from the spaces ℓk(F(B)) and ℓ∞(F(B)) to space Y∈ { ℓ∞, c, c, ℓ1, cs, cs, bs} and obtain the necessary and sufficient condition for a matrix operator to be compact from the spaces ℓk(F(B)) and ℓ∞(F(B)) to Y∈ { ℓ∞, c, c, ℓ1, cs, cs, bs} using the Hausdorff measure of non-compactness.