Subdivisions of the Spectra for the Triple Band Matrix over Certain Sequence Spaces

In a series of papers, B. Altay, F. Başar and A.M. Akhmedov recently investigated the spectra and fine spectra for difference operator, considered as bounded operator over various sequence spaces. In the present paper approximation point spectrum, defect spectrum and compression spectrum of an operator represented by the triple band matrix B(r,s,t) over the sequence spaces c0, c, ℓp and bvp are determined, where bvp denotes the space of all sequences xk such that (xk –xk-1) belongs to the sequence space ℓp with 1≤p≤∞ and was studied by Başar and Altay [Ukrainian Math. J., 55(1) (2003), 136-147].