Definition 13.12.3 (Injective Tensor Product).label Let $E, F$ be locally convex spaces over $K \in \RC$, and identify $E \otimes F$ as a subspace of $L^{2}(E, F; K)$, then $E \otimes F$ equipped with the topology of bi-equicontinuous convergence is the injective tensor product of $E$ and $F$, denoted $E \otimes_{\eps} F$.

The Hausdorff completion $E \wh{\otimes}_{\eps} F$ of $E \otimes_{\eps} F$ is the injective completion of $E$ and $F$.