Geodesic
Spectra of the Lower Triangular Matrix $\mathbb B(r_1,\dots, r_l; s_1,\dots, s_l')$ over $c_0$
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 369

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The infinite lower triangular matrix $\mathbb{B}(r_1,dots,r_l;s_1,dots,s_{l'})$ is considered over the sequence space $c_0$, where $l$ and $l'$ are positive integers. The diagonal and sub-diagonal entries of the matrix consist of the oscillatory sequences $r=(r_{k (\text{mod} \ l)+1})$ and $s= (s_{k(\text{mod} \ l')+1})$, respectively. The rest of the entries of the matrix are zero. It is shown that the matrix represents a bounded linear operator. Then the spectrum of the matrix is evaluated and partitioned into its fine structures: point spectrum, continuous spectrum, residual spectrum, etc. In particular, the spectra of the matrix $\mathbb{B}(r_1,dots, r_4; s_1,dots, s_{6})$ are determined. Finally, an example is taken in support of the results.
Classification : 47A10, 47B37
Keywords: fine spectra, sequence space, lower triangular infinite matrix, point spectrum, continuous spectrum, residual spectrum 
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     title = {Spectra of the {Lower} {Triangular} {Matrix} $\mathbb B(r_1,\dots, r_l; s_1,\dots, s_l')$ over $c_0$},
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Sanjay Kumar Mahto; Arnab Patra; P. D. Srivastava. Spectra of the Lower Triangular Matrix $\mathbb B(r_1,\dots, r_l; s_1,\dots, s_l')$ over $c_0$. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 369 . http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a2/