On the fine spectra of triple-band matrix U(r,s,t) over the sequence space l_1

In functional analysis, the spectrum of an operator generalizes the notion of eigenvalues for matrices. The spectrum of an operator over a Banach space is partitioned into three parts, which are the point spectrum, the continuous spectrum and the residual spectrum. The calculation of three parts of the spectrum of an operator is called calculating the fine spectrum of the operator. The fine spectra of lower triangular double and triple - band matrices have been examined by several authors. Karakaya and Altun (2010) have determined the fine spectra of upper triangular double-band matrices over the sequence spaces c_0 and c. Here we determine the fine spectra of upper triangular triple-band matrix U(r,s,t) over the sequence space l_1.