If $S, T$ are self-adjoint operators on a Hilbert space $H$, then we can say that $S\geq T$ when $S-T$ is positive semi-definite operator.
This ordering, in general, doesn't form a lattice.
My question is, does this order belong to some neat class of orders? That is, can we derive some property (or properties) of orders so that the order belongs to them (of course I'm looking for something non-trivial)?