The serpentine belt tensioner on my 2003 Corolla

Not sure if you mean the pulley is seized or the tensioning system is seized.
If you are trying to take the belt off and can not as it appears the tensioning system is seized, place a long handle wrench on the adjust nut that is formed in the tensioner, then double wrench another long handle wrench on the end of it.
Instead of trying to pull the tensioner to release the belt, place solid steady pressure on the wrench and wait for it to slowly collapse. It is a fluid filled shock that holds it in place and requires constant firm pressure to release; it will not just bend out of the way by pulling on a wrench like normal tensioners.

I have never seen on seize before, and the design of it makes it very difficult for this to happen, I have seen this complaint before though and it was just the design of the system that makes it appear stuck.

If it is in fact stuck, removal is best left to a shop, as it is very advantageous to have a lift so you can work underneath the vehicle safely; it is a very tight fit removing these tensioners.
If you do need the tensioner and you decide to do it yoruself, (only two bolts holding it on), besure to manually pump the tensioner 3 full sweeps before installing the belt, or the hydraulic unit may fail prematurely.

If you have any questions please ask before rating me so I can help you further and earn a good rating. I am always happy to elaborate.