Rozendaal, JanVeraar, Mark2023-03-132023-03-131424-3199http://hdl.handle.net/1885/287002We study growth rates for strongly continuous semigroups. We prove that a growth rate for the resolvent on imaginary lines implies a corresponding growth rate for the semigroup if either the underlying space is a Hilbert space, or the semigroup is asymptotically analytic, or if the semigroup is positive and the underlying space is an 𝐿𝑝-space or a space of continuous functions. We also prove variations of the main results on fractional domains; these are valid on more general Banach spaces. In the second part of the article, we apply our main theorem to prove optimality in a classical example by Renardy of a perturbed wave equation which exhibits unusual spectral behavior.application/pdfen-AU© 2018 The authorshttp://creativecommons.org/licenses/by/4.0/201810.1007/s00028-018-0459-x2021-12-26Creative Commons Attribution licence