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Subdivision of Spectra for Some Lower Triangular Double-Band Matrices as Operators on c0

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Ukrainian Mathematical Journal Aims and scope

The generalized difference operator ∆a,b was defined by El-Shabrawy:

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

where (ak) and (bk) 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 c0.

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Authors and Affiliations

  1. Cumhuriyet University, Sivas, Turkey

    N. Durna

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  1. N. Durna
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 7, pp. 913–922, July, 2018.

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Durna, N. Subdivision of Spectra for Some Lower Triangular Double-Band Matrices as Operators on c0. Ukr Math J 70, 1052–1062 (2018). https://doi.org/10.1007/s11253-018-1551-7

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  • DOI: https://doi.org/10.1007/s11253-018-1551-7

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