Legal Question in Criminal Law in Ohio

The notice is from the property owner (or lessee), not the court. The owner has the right to ban you from the premises, and he has invoked that right. You do not have the right to enter against the owner's wishes. If you do so, you will be a trespasser subject to arrest and/or forcible removal. The courts will not help you, since you have to right to enter someone else's private property without permission.

(Please note that my answer presumes you were not banned because of your race, religion, etc. Such a ban might be illegal. But you seem to have been banned due to your conduct. The owners have every right to do that.)

But if the notice came from a single business within a large complex, it probably forbids you only from entering the premises of that business. The owner of one business probably cannot ban you from other businesses in the same complex, though I suppose the owner of the complex and/or the owners of the other businesses might have given him such authority.

I need to correct a typo in my prior response. The last sentence of the first paragraph should have said "The courts will not help you, since you have no right to enter someone else's private property without permission." I had mistakenly written "to" instead of "no".