Good point, I do not know. Perhaps a lawyer person on Free Republic can clarify this point?
Its their property. They can make whatever “rule” they like. If you break their “rules” they can ask you to leave.
If you then refuse to leave, that is misdemeanor trespassing.
But carrying into a business that proclaims itself “gun free”? That’s not illegal. Their rule or policy is a mere suggestion. Treat it as such. I do.