Abstract.
Given the generator −A of a holomorphic semigroup on a Hilbert space H, we show that A is associated with a closed form if and only if \(A+w\in BIP(H)\) for some \(w\in\Bbb{R}\). Under this condition we also show that Liapunov's classical theorem is true, in the linear as well as the semilinear case.
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Received: 8.2.2001
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Arendt, W., Bu, S. & Haase, M. Functional calculus, variational methods and Liapunov's theorem. Arch. Math. 77, 65–75 (2001). https://doi.org/10.1007/PL00000467
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DOI: https://doi.org/10.1007/PL00000467