Geodesic
On estimates of eigenvalues of infinite block tridiagonal matrices
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 118-126

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In this paper, we study the operators generated by infinite tridiagonal block matrices under the condition that the spectrum of the corresponding diagonal matrix is separated. Using the method of similar operators, we obtain conditions that provide the diagonalizability of the original operator (or its block diagonalizability). Also, we obtain the asymptotics of the weighted means of the eigenvalues of such operators.
Keywords: eigenvalue, method of similar operators, infinite block tridiagonal matrix. 
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     author = {G. V. Garkavenko and N. B. Uskova},
     title = {On estimates of eigenvalues of infinite block tridiagonal matrices},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
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G. V. Garkavenko; N. B. Uskova. On estimates of eigenvalues of infinite block tridiagonal matrices. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 118-126. http://geodesic.mathdoc.fr/item/INTO_2021_195_a13/