Geodesic
Conditions for invertibility and Hurwitz stability
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 84-89

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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 
@article{FAA_2017_51_4_a8,
     author = {A. I. Perov},
     title = {Conditions for invertibility and {Hurwitz} stability},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {84--89},
     publisher = {mathdoc},
     volume = {51},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a8/}
}
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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/