There is no directly applicable law on such things like there are for firearms. Rather, it's based on other legal principles.
If it's really private property and not a government facility of some kind, it's based on the rights of the owner to refuse service and/or entry. Businesses can refuse entry to anyone for any reason other than those covered by discrimination laws (which are based on attributes of the person that they cannot change, rather than objects they carry or their behavior). The guard cannot arrest you for having a knife, he can simply turn you away or ask you to leave the premises if you are found to have something after entry. If you refuse to leave, you are trespassing, rather than violating any kind of weapon-related law, and can be arrested.
This same principle can also be applied to firearms, but most states have special laws that amend how it works, and these can be go either way. For example, some states prohibit firearms in certain kinds of business like bars or places where alcohol is served. Others have it in the statute that if the business has a sign displayed that meets certain specs, carry of a firearm within is a crime. Still others have more pro-gun provisions, such as a few states where you cannot prohibit people with carry permits to bring their guns inside unless you have metal detectors (since criminals will just bring theirs in anyway if you have no actual way to prevent it). But as far as I know, there are no such special provisions for knives.
