Geodesic
Conditions for invertibility and Hurwitz stability
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 84-89 Cet article a éte moissonné depuis la source Math-Net.Ru

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In a generalization of Fiedler's theorem, a block condition for the invertibility of an operator and an estimate for the operator matrix of the inverse operator are presented. A block condition for an operator to be Hurwitz is also given, which contains an estimate of the spectral abscissa of the operator.
Keywords: Banach space, bounded linear operator, Lozinskii logarithmic norm, invertible operators and the block invertibility condition (Fiedler's theorem), Hurwitz operators and a block condition for Hurwitz stability.
Mots-clés : spectral abscissa 
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     title = {Conditions for invertibility and {Hurwitz} stability},
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A. I. Perov. Conditions for invertibility and Hurwitz stability. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 84-89. http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a8/

[1] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975 | MR

[2] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1967 | MR

[3] B. A. Sevastyanov, UMN, 6:6 (1951), 47–99 | MR | Zbl

[4] M. Kamenskii, P. Nistri, Set-Valued Analysis, 11:4 (2003), 345–357 | DOI | MR | Zbl

[5] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980 | MR

[6] B. F. Bylov, R. E. Vinograd, D. M. Grobman, V. V. Nemytskii, Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti, Nauka, M., 1966 | MR

[7] Yu. L. Daletskii, M. G. Krein, Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[8] E. Bekkenbakh, R. Bellman, Neravenstva, Mir, M., 1965 | MR