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

The spectra and fine spectra of the lower triangular matrix $\mathbb{B}$ $(r_1,\dots ,r_l;$ $s_1,\dots ,s_{l^{\mathrm{\prime }}})$ 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.