I think some Leos might point out that a "properly" worded sign does constitute a request from management. Now if the cop walking into the mall is not already doing so on official business then he could also be subject to trespassing.
I think the "official business" exception applies to railroad trespass/common carrier. As far as other property is concerned, I don't see an official business exemption. So if no guns are posted, and the officer enters, sounds like he has to arrest himself.