A Note on the Spectra of Forward Difference Operator on the Sequence Space l1

In this work, we compute the fine spectra of the forward difference operator ∆μ+ on l1, where μ = (μk) is a positive real sequence of non-increasing terms satisfying certain conditions. The point spectrum, the residual spectrum, the continuous spectrum, the spectrum and some fine spectra of the operator ∆μ+ on the Banach space l1 are computed which give a natural modifications of the results obtained in [7] and [11]. In this context, some illustrative examples are also provided