Fine Spectrum Of The Generalized Difference Operator Delta(Uv) On The Sequence Space C(0)

The purpose of this paper is to determine spectrum and fine spectrum of the operator Delta(uv) on the sequence space c(0). The operator Delta(uv) on sequence space c(0) is defined as Delta(uv)x = (u(n)x(n)+v(n-1)x(n-1))(n=0)(infinity) satisfying certain conditions, where x(-1) = 0 and x = (x(n)) is an element of c(0). In this paper we have obtained the results on the spectrum and point spectrum for the operator Delta(uv) on the sequence space c(0). Further, the results on continuous spectrum, residual spectrum and fine spectrum of the operator Delta(uv) on sequence space c(0) are also derived.