There is a beam that runs down the center of our house (in the basement). Floor joists are hung on both sides of this beam. On one side of the beam there are gaps between the subfloor and joists (see pic below), but the joists are all level. The max gap is about 3/8". I don't know if it matters, but the joists are not sitting directly on the hangars either (there's a slight gap, see second pic). This gap has led to the subfloor saging and squeaking when people walk on it. I'm concerned that this will lead to damage to the subfloor or the hardwood floor that's on top of it.
How can I fill in this gap and support the subfloor? My first thought was to put shims in there, but I don't know if there's a bigger problem here. If shims are good enough, then I assume I'll have to fill in the entire gap (i.e., just putting 1 in at the beam will not suffice).