Topologies on the set of operators on a Hilbert space
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In mathematics, the requirements of functional analysis mean there are several standard topologies which are given to the set of bounded linear operators on a Hilbert space.
- norm topology
- ultrastrong topology
- strong operator topology (SOT)
- weak operator topology (WOT)
- weak-star operator topology
- ultraweak topology
Some facts
The norm topology is stronger than the strong operator topology which is stronger than the weak operator topology.
The norm topology is stronger than the weak-star topology which is stronger than the weak operator topology.
The closures of a convex set in the strong and the weak operator topologies coincide.
The weak operator topology and the weak-star topology agree on norm-bounded sets.
See also: