Geodesic
On equivalent operators
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—XXXV", Voronezh, April 26-30, 2024, Part 1, Tome 235 (2024), pp. 3-14

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In this paper, we introduce the concept of equivalent operators, i.e., operators with the same invertibility states, and establish their connection with weakly similar and similar operators. We find the invertibility states of some classes of linear operators, in particular, operators with involution and operators with compact resolvent. We discuss approaches to constructing equivalent operators and give examples of equivalent operators.
Keywords: invertibility states, equivalent operators, strongly equivalent operators, weakly similar operators, similar operators 
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     title = {On equivalent operators},
     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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A. G. Baskakov; G. V. Garkavenko; N. B. Uskova; L. N. Kostina. On equivalent operators. 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—XXXV", Voronezh, April 26-30, 2024, Part 1, Tome 235 (2024), pp. 3-14. http://geodesic.mathdoc.fr/item/INTO_2024_235_a0/