On the Fine Structure of Spectra of Upper Triangular Double-Band Matrices as Operators on ℓp Spaces

In the present paper, we study the fine structure of spectra of infinite upper triangular double-band matrices as operators on ℓp, where 1 ≤ p < ∞. Three methods for classifying the spectrum are considered. Moreover, the obtained results are used to study the eigenvalue problem associated with certain infinite matrices. Our results improve and generalize many known results in the current literature