Please allow me to clarify the confusion expressed above about Texas carry law.
If you have a Texas License To Carry (LTC) or any CHL recognized by reciprocity (including Illinois BTW), you cannot be prohibited from carrying anywhere, with two exceptions. Those places statutorily prohibited (e.g. schools, etc.), or private property where the owner has posted the exact state prescribed signage. Specifically the 30.06 (concealed) or 30.07 (open carry) sign. If you do not post these signs, your corporate policy, gun buster sign or whatever you post has no force of law. Public places, not statutorily prohibited, are not allowed to post. Parking lots are not considered premises and must be posted separately, they rarely are, I've never seen one. Even employers who prohibit possession cannot enforce carry in your vehicle in their parking lots.
So, while Simon Malls may have a corporate policy, their stores in Texas are not posted, so they are not gun free zones, especially for licensed concealed carry.
The only other exception is that if a proprietor (who has not posted) discovers you are carrying, they can ask you to leave. If you do not leave, you are considered trespassing, and that can cause the appearance of LE.
With Constitutional Carry, it is a bit more interesting. The only way a proprietor can prohibit constitutional carry, is to post "no trespassing with guns signs". Note that these signs have absolutely no bearing on a licensed carrier and no force of law on them. If the licensed carrier is discovered, they can be asked to leave, but they cannot be prosecuted for violating the "no trespassing" sign.
Hope this helps