What would a UV Sterilizer do for me?

A UV sterilizer kills waterborne pathogens and microorganisms such as bacteria, plankton, and suspended algae. Whether you need to accomplish this in your tank is another matter. I use one on my pond because it's in full sun so the water turns green otherwise. They are unnecessary on a properly maintained inside tank, IMO.
 
The main benefits is provides is the radical decomposition of various organic molecules in the water, resulting in much clearer water. Secondarily, it does a reasonably good job at reducing bacteria and small algae concentrations. It is not very effective at controlling larger organisms, like ich and the like.
 
It's doubtful that it will be of much help. It would be different if it were a planktonic algae problem (akin to "green water"), but it is not. You need to look into nitrate and phosphate levels to solve your particular problem. Adding some extra water flow can also help in many situations.
 
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