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.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.3$: The normed space $\map {CL} {X, Y}$. Strong and weak operator topologies on $\map {CL} {X, Y}$