Proposition 10.13.3 ([IV.4.3, SW99]).label Let $E, F$ be TVSs over $K \in \RC$ and $\alg \subset L(E; F)$ be equicontinuous, and $\alg'$ be the closure of $\alg$ in $F^{E}$ with respect to the product topology, then $\alg'$ is equicontinuous and hence $\alg' \subset L(E; F)$.