Displaying similar documents to “Corrigendum to “On the spectral bound of the generator of a C 0 -semigroup” (Studia Math. 125 (1997), 23-33)”

On the exponential stability and dichotomy of C 0 -semigroups

Phóng Vũ (1999)

Studia Mathematica

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A characterization of exponentially dichotomic and exponentially stable C 0 -semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.

Closed semistable operators and singular differential equations

Jaromír J. Koliha, Trung Dinh Tran (2003)

Czechoslovak Mathematical Journal

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We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which 0 is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of C 0 -semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions...