Abstract:
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, spectral abscissa, Lozinskii logarithmic norm, invertible operators and the block invertibility condition (Fiedler's theorem), Hurwitz operators and a block condition for Hurwitz stability.
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