Geodesic
Method of similar operators in the problem of bi-invariant subspaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 3-15

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In this paper, we discuss the construction of bi-invariant subspaces for a self-adjoint, linear, closed operator with discrete spectrum perturbed by a bounded operator. The main result is the theorem on the similarity of this operator to a block diagonal operator. This theorem implies results concerning biinvariant subspaces and formulas for projectors and weighted average eigenvalues. In addition, we construct the corresponding group of operators and propose a new modification of the method of similar operators.
Keywords: method of similar operators, spectral projectors
Mots-clés : biinvariant subspaces. 
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     title = {Method of similar operators in the problem of bi-invariant subspaces},
     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},
     volume = {204},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_204_a0/}
}
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A. G. Baskakov; G. V. Garkavenko; I. A. Krishtal; N. B. Uskova. Method of similar operators in the problem of bi-invariant subspaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI". Voronezh, May 3-9, 2020, Tome 204 (2022), pp. 3-15. http://geodesic.mathdoc.fr/item/INTO_2022_204_a0/