1. How much sunlight is your tank getting? Many of the green water algae blooms that friends have had (I have never had one - hair algae is my recurrent problem) occur when the tank is getting natural sunlight (doesn't have to even summer or direct light).
2. A UV sterilizer will help with green water, but it is still better to find and fix the source of the problem. What are your nitrates and phospates? High levels can promote algae growth.
3. A product called Filter-Aid that you put on your mechanical filter floss will help aggregate the suspended algae particles. However, you do want to clean the filter frequently to avoid all that algae die-off at once which can be a tank killer.