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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Two counterexamples in semigroup theory on Hilbert space
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by Paul R. Chernoff PDF
Proc. Amer. Math. Soc. 56 (1976), 253-255 Request permission

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
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 253-255
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0399952-4
  • MathSciNet review: 0399952