Definition:Uniform Operator Topology

Definition
Let $\struct {X, \norm {\, \cdot \,}_X}$ and $\struct {Y, \norm{\, \cdot \,}_Y}$ be normed vector spaces.

Let $\map {CL} {X, Y}$ be the continuous linear transformation space.

Let $\norm {\, \cdot \,}$ be the supremum operator norm.

Then the topology induced by $\struct {\map {CL} {X, Y}, \norm {\, \cdot \,}}$ is called the uniform operator topology.