Aquarium UV sterilisers are not aimed at reducing green water and algae, but to reduce free floating organisms and pathogens. The most obvious target is Ich. Most aquariums sterilisers actually say on the box that they are not for reducing algae.
It can be especially useful in tanks that are large, and thus treating with meds becomes very expensive and a bit hit and miss. People argue about how effective they are, but I had a fairly nasty outbreak and the UVs demolished the ich within a week. I have never had a problem since (and many new fish have been added).
I would always recommend them on a large tank due to the above.