On a Spectral Subdivision of the Operator Δ_i^2 over the Sequence Spaces c_0 and _1: P. Baliarsingh, S. Dutta - Team, Support (Thai Journal of Mathematics, 2019)
The main objective ofthis paper is to determine the spectrum and the fine spectrum ofthe difference operator Δ_i^2 over the sequence spaces c_0 and _1. For any sequence x=(x_k) in c_0 or _1, the generalized difference operator Δ_i^2 over c_0 or _1 is defined by (Δ_i^2(x))_k =_i=0^2(-1)^ii+12ix_k-i=x_k-x_k-1+13x_k-2, with x_k = 0 for k < 0. Moreover, we compute the spectrum, the point spectrum, the residual spectrum and the continuous spectrumof the difference operator Δ_i^2 over the basic sequencespaces c_0 and _1.