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 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

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 
@article{KJM_2022_46_3_a2,
     author = {Sanjay Kumar Mahto and Arnab Patra and P. D. Srivastava},
     title = {Spectra of the {Lower} {Triangular} {Matrix} $\mathbb B(r_1,\dots, r_l; s_1,\dots, s_l')$ over $c_0$},
     journal = {Kragujevac Journal of Mathematics},
     pages = {369 },
     year = {2022},
     volume = {46},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a2/}
}
TY  - JOUR
AU  - Sanjay Kumar Mahto
AU  - Arnab Patra
AU  - P. D. Srivastava
TI  - Spectra of the Lower Triangular Matrix $\mathbb B(r_1,\dots, r_l; s_1,\dots, s_l')$ over $c_0$
JO  - Kragujevac Journal of Mathematics
PY  - 2022
SP  - 369 
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a2/
LA  - en
ID  - KJM_2022_46_3_a2
ER  - 
%0 Journal Article
%A Sanjay Kumar Mahto
%A Arnab Patra
%A P. D. Srivastava
%T Spectra of the Lower Triangular Matrix $\mathbb B(r_1,\dots, r_l; s_1,\dots, s_l')$ over $c_0$
%J Kragujevac Journal of Mathematics
%D 2022
%P 369 
%V 46
%N 3
%U http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a2/
%G en
%F KJM_2022_46_3_a2
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/