Spectra of the lower triangular matrix $\mathbb{B}(r_1,\dots , r_l; s_1, \dots, s_{l'})$ over $c_0$

Abstract

The spectra and fine spectra of the lower triangular matrix $\mathbb{B}$ $(r_1,\dots , r_l;$ $ s_1, \dots, s_{l'})$ over the sequence space $c_0$ are determined. The diagonal and sub-diagonal entries of the matrix consist of two oscillatory sequences $r=(r_{k (\text{mod} \ l)+1})$ and $s= (s_{k(\text{mod} \ l')+1})$ respectively, whereas the rest of the entries of the matrix are zero. In particular, the spectra and fine spectra of the lower triangular matrix $\mathbb{B}(r_1,\dots , r_4; s_1, \dots, s_{6})$ over $c_0$ are discussed.