Fine Spectrum of the Generalized Difference Operator Δ_uv on the Sequence Space c_0: Parmeshwary Dayal Srivastava, Sudhanshu Kumar - Team, Support (Thai Journal of Mathematics, 2018)
The purpose of this paper is to determine spectrum and fine spectrum of the operator Δ_uv on the sequence space c_0. The operator Δ_uv on sequence space c_0 is defined as Δ_uv x=(u_n x_n + v_n-1 x_n-1)_n=0^∞ satisfying certain conditions, where x_-1=0 and x=(x_n) c_0. In this paper we have obtained the results on the spectrum and point spectrum for the operator Δ_uv on the sequence space c_0. Further, the results on continuous spectrum, residual spectrum and fine spectrum of the operator Δ_uv on sequence space c_0 are also derived.