Exercise 8, § 4

Tag 034S, permanent. Cite it as [Bourbaki, Tag 034S].

Spectral Theories, IV, p. 347

Let E be a complex Banach space. Let $s$ be a contracting continuous semigroup on E, and let $u$ be its infinitesimal generator. Then

(t)^{-n}

lim 1 + $ux=s(t)x$

_{n\rightarrow+\infty}n

for all $x\in E$ .

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