As has been posted, on private property the property owner or their agent can request that no firearms be carried. If you violate their policy with CCW and they somehow find out, they are within their rights to ask you to leave the premises (they can do that anyway), and once you've been notified of their policy carrying anyway might subject you to a trespassing charge.
Generally there's no way for the property owner (in this case, the mall security?) to determine if you've got a CCW - but it would serve to prevent open carry on those premises. In states which allow unrestricted open carry (except for schools, government buildings, bars, churches, usually), posting a no firearms notice is the only legal recourse a property owner has to prevent the display of weapons on their premises. Needless to say, if you're practicing open carry, you probably will get asked to leave if you ignore the sign and carry openly anyway.