# Subdivision of Spectra for Some Lower Triangular Double-Band Matrices as Operators on *c*_{0}

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The generalized difference operator ∆where (

_{a,b}was defined by El-Shabrawy:$$ {\varDelta}_{a,b}x={\varDelta}_{a,b}\left({x}_n\right)={\left({a}_n{x}_n+{b}_{n-1}\right)}_{n=0}^{\infty}\;\mathrm{with}\;{x}_{-1}={b}_{-1}=0, $$

*a*_{k}) and (*b*_{k}) are convergent sequences of nonzero real numbers satisfying certain conditions. We completely determine the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator ∆_{a,b}in a sequence space*c*_{0}*.*## Preview

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