The fine spectra of lower triangular triple-band matrices have been examined byseveral authors (e.g., Akhmedov (2006), Başar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence spaceℓp. The operatorA(r,s,t)on sequence space onℓpis defined byA(r,s,t)x=(rxk+sxk+1+txk+2)k=0∞, wherex=(xk)∈ℓp, with0<p<∞. In this paper we have obtained the results on the spectrum and point spectrum for the operatorA(r,s,t)on the sequence spaceℓp. Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operatorA(r,s,t)on the sequence spaceℓpare also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operatorA(r,s,t)over the spaceℓpand we give some applications.
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