> [!definition] > > Let $E, F$ be [[Locally Convex Topological Vector Space|locally convex topological vector spaces]] and $L(E, F)$ be the space of [[Continuous Linear Map|continuous linear maps]] from $E$ to $F$. For each $x \in E$ and $\phi \in F^*$, the mapping > $ > [\cdot]_{x, \phi}: L(E, F) \to \real^+ \quad T \mapsto \abs{\angles{x, \phi}_F} > $ > is a [[Seminorm|seminorm]]. The topology on $L(E, F)$ induced by $\bracs{[\cdot]_{x, \phi}: x \in E, \phi \in F^*}$ is the **weak operator topology**, corresponding to pointwise [[Weak Topology|weak]] convergence.