Definition 10.5.2 (Continuous Multilinear Map).label Let $\seqf{E}$, $F$ be TVSs over $K \in \RC$, then the set $L^{n}(E_{1}, \cdots, E_{n}; F) = L^{n}(\seqf{E_j}; F)$ is the space of all continuous $n$-linear maps from $\prod_{j = 1}^{n} E_{j}$ to $F$.