Spectrum and fine spectrum of the upper triangular triple-band matrix over some sequence spaces

Abstract

The fine spectra of lower triangular triple-band matrices in some sequence spaces was examined by several authors. Recently, Karakaya and Altun determined the fine spectra of upper triangular double-band matrices over the sequence spaces c0 and c, in [1]. In this paper, we determine the fine spectra of the upper triangular triple-band matrix over the sequence spaces c0, c and l∞. Additionally, we give the approximate point spectrum, the defect spectrum and the compression spectrum of the matrix operator A(r, s, t) over the spaces c0, c and l∞ with some applications. These results are more general than the corresponding results obtained by Karakaya and Altun [J. Comput. Appl. Math. 234 (2010), 1387–1394].