After you ban someone for being an abusive creep, you need to let the community know you've banned them for being an abusive creep. If you don't, then they'll contact other members off-site and continue the abuse. When you do, you'll get many more reports as people now feel empowered to come forward, and you'll feel like crap because you didn't know this person was doing these awful things.
You'll also get lots of angry messages of disbelief because abusers are always funny and charming.