This has been said above, I am sure, but it bears repeating. If the neighbor is simply opening and closing his door and it makes a lot of noise, then it's not the neighbor you have the problem with. Take this up with the building management so that they repair the obviously-malfunctioning door.
You could even turn this in to a positive neighborly experience by having all of the neighbors (the downstairs neighbor included) sign the same letter of complaint so that management knows this is not just an over-sensitive person complaining. You could work with the guy to help make his (and everyone else's) life better.