If $x\in B(H)$ and $x=x^*$, then the support $s(x)$ of $x$ can be defined as following:
$s(x)$ is the smallest projection $e\in B(H)$ such that $ex=x=xe$.
If $x$ is an unbounded self-adjoint operator, how to define the support projection of $x$?
More precisely, if $x$ is a self-adjoint unbounded operator which is affiliated with a von Neumann algebra $M$. If we take the above definition, we cannot assure that $s(x)x$ make sense.