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On the spectral mapping theorem for perturbed strongly continuous semigroups

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Abstract.

We consider a strongly continuous semigroup \((T(t))_{t \geqq 0}\) with generator A on a Banach space X, an A-bounded perturbation B, and the semigroup \((S(t))_{t \geqq 0}\) generated by A + B. Using the critical spectrum introduced recently, we improve existing spectral mapping theorems for the perturbed semigroup \((S(t))_{t \geqq 0}\) .

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  1. Arbeitsbereich Funktionalanalysis, Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, , , , , , DE

    S. Brendle, R. Nagel & J. Poland

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  1. S. Brendle
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  2. R. Nagel
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  3. J. Poland
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Received: 22.12.1998

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Brendle, S., Nagel, R. & Poland, J. On the spectral mapping theorem for perturbed strongly continuous semigroups. Arch. Math. 74, 365–378 (2000). https://doi.org/10.1007/s000130050456

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  • DOI: https://doi.org/10.1007/s000130050456

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