I can understand where you are coming from with this. Recently I was dropping my wife off at the mall while I was carrying. I did remove my pistol and lock in the car until I had proof that I was good to go. When I got to the door there was no sign posted on the exterior of the doors or entrance anywhere. After getting past the second set of doors there was a code of conduct sign in a free standing poster holder as you enter. After reading that and getting to point #3 it did state that weapons up to and including firearms were not permitted on the premises.
I am very curious what the legalities of this are. As you walk in there, there is also a security desk where the Toledo Police work security along with the mall security. I've not challenged the sign as of yet.