Solvability of some perturbed sequence spaces equations with operators


Bruno De Malafosse, Ali Fares, Ali Ayad




In this paper, we apply the results stated in [19] to the solvability of the sequence spaces equations (SSE)E+Fx = Fb, whereE,F are linear spaces of sequences and b, x are positive sequences (x is the unknown). In this way, we solve the (SSE) of the form (Ea)G(α,β) + Fx = Fb, where G ( α, β ) is a factorable triangle matrix defined by [ G ( α, β )] nk = αnβk for k ≤ n and (E,F) ∈ {(`∞, c) , (c0, `∞) , (c0, c) , (`p, c) , (`p, `∞) , (w0, `∞)}with p ≥ 1. Then we deal with some (SSE) involving the matrices C (λ), C1 and Nq. Finally, we solve the (SSE) with operator of the form (Ea)Σ2 + Fx = Fb,