Locally Finite-Dimensional Sets of Operators
Leonya Livshits · Proceedings of the American Mathematical Society · 1993
For any pair of Banach spaces $V$ and $W$ a "global" description is given for the sets $S$ of operators in $B(V,W)$ satisfying the "local" condition that the linear span of the set $\{ T(x)|T \in S\}$ is finite-dimensional for every $x$ in $V$.