Definition 13.7.1 (Compact Operator).label Let $E, F$ be locally convex spaces over $K \in \RC$ and $T \in L(E; F)$, then $T$ is compact if there exists $U \in \cn_{E}(0)$ such that $T(U)$ is relatively compact in $F$.

The set $\mathcal{K}(E; F)$ is the space of compact operators from $E$ to $F$.