Are finite rank operators on Hilbert space $H$ dense in $B(H)$ in the weak operator topology?
Density of finite rank operators on Hilbert space
4
$\begingroup$
functional-analysis
operator-theory
-
2In the second part of my answer [here](http://math.stackexchange.com/a/126863) I show that the finite rank operators (it suffices to take those which are nilpotent of index 2) are strongly dense in $B(X)$ whenever $X$ is a Banach space. Since the weak topology is weaker than the strong topology on $B(H)$ it follows that the finite rank operators are weakly dense in $B(H)$ whether $H$ is separable or not. – 2012-06-28