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Two counterexamples in semigroup theory on Hilbert space


Author: Paul R. Chernoff
Journal: Proc. Amer. Math. Soc. 56 (1976), 253-255
DOI: https://doi.org/10.1090/S0002-9939-1976-0399952-4
MathSciNet review: 0399952
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Abstract | References | Additional Information

Abstract: There exist $ ({C_0})$ semigroups $ {T_1}(t),{T_2}(t)$ on Hilbert space with the following properties: $ {T_1}$ has a bounded generator and is uniformly bounded, but is not similar to a contraction semigroup. $ {T_2}$ is uniformly bounded, and there exists no scalar $ \alpha $ such that $ {e^{ - \alpha t}}{T_2}(t)$ is similar to a contraction semigroup.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399952-4
Article copyright: © Copyright 1976 American Mathematical Society

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