Corollary

Let $\varrho$ be a continuous representation of G in a separated locally convex K-vector space E. The contragredient representation $\breve{\varrho}$ is continuous when $E'$ is endowed with the topology of compact convergence.

This results from the proposition by taking $H =\{e\},\varrho_1=\varrho$ and $\varrho_2$ the trivial representation on K.