The space can never be compact in any topology, because it is unbounded. For example, the sequence (nI), where I is the identity operator, cannot have a convergent subsequence.
The unit ball of is compact in the weak operator topology.
The space can never be compact in any topology, because it is unbounded. For example, the sequence (nI), where I is the identity operator, cannot have a convergent subsequence.
The unit ball of is compact in the weak operator topology.