Fine Spectra of Upper Triangular Triple-Band Matrices over the Sequence Space lp ( 0 < p < ∞)

The fine spectra of lower triangular triple-band matrices have been examined by several authors (e. g., Akhmedov (2006), Basar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space l(p). The operator A(r, s, t) on sequence space on l(p) is defined by A(r, s, t)x = (rx(k) + sx(k+1) + tx(k+2))(k=0)(infinity), where x = (x(k)) is an element of l(p), with 0 < p < infinity. In this paper we have obtained the results on the spectrum and point spectrum for the operator A(r, s, t) on the sequence space l(p). Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator A(r, s, t) on the sequence space l(p). are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator A(r, s, t) over the space l(p) and we give some applications.