Geodesic
On spectral properties of one difference operator with involution
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 15-23

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We consider a difference operator with involution acting in the complex Hilbert space $l_2(\mathbb{Z})$. Using the method of similar operators, we reduce it to the diagonal (block diagonal) form, which allows one to obtain various spectral characteristics of the original operator and to construct biinvariant subspaces for it.
Keywords: method of similar operators, difference operator, spectrum, spectral projector. 
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     title = {On spectral properties of one difference operator with involution},
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G. V. Garkavenko; N. B. Uskova. On spectral properties of one difference operator with involution. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 15-23. http://geodesic.mathdoc.fr/item/INTO_2022_208_a2/