Remark 3

Tag 09II, permanent. Cite it as [Bourbaki, Tag 09II].

Integration, VIII, p. 9, § 2. Linear representations of groups

Suppose that $U$ is a continuous linear representation of $G$ in $E$ . For every $s \in G$ , let $\widehat{U}(s)$ be the continuous extension of $U(s)$ to the completion $\widehat{E}$ of $E$ . Then $\widehat{U}$ is a linear representation of $G$ in $\widehat{E}$ , satisfying conditions a) and c) of Remark 2, and also condition b) by GT, X, §2, No. 2, Prop. 4. Therefore $\widehat{U}$ is a continuous linear representation of $G$ in $\widehat{E}$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

X, §2, No. 2, Prop. 4 not yet on this site
Remark 2