A few examples that come immediately to mind:
There are laws that make it a crime to own a large percentage of the stock of a company without disclosing it.
An ownership interest in a "corrupt" organization is a racketeering offense.
It is illegal to own nuclear materials (which are as a matter of law the property of the United States government) or non-prescribed controlled substances or certain disease causing pathogens or a merchant ship without a license. It is illegal to own an operating taxi cab without a license. It is illegal to own certain devices for cheating ATMs and cable/satellite TV systems. It is illegal to own many kinds of ivory without a license, and it is illegal to own Bald Eagle parts without a license, and in some cases to own conflict diamonds. It is illegal to own body parts for transplantation (except to the extent that you own yourself when they are transplanted into you).
Ownership of people is generally prohibited (this is called "human trafficking", "slavery" or "peonage"). Many kinds of ideas are not capable of ownership as intellectual property.
Ownership of many kinds of animals is permitted only with an appropriate license.
There are elaborate regulations governing ownership of legal marijuana businesses, of liquor stores, of casinos, of medical practices and of legal practices, to name a few. Ownership of property necessary to carry on such businesses would be a violation.
Some states prohibit people other than natural persons or general partnerships from owning farms.
Many countries, such as Mexico, prohibit foreigners from certain kinds of land ownership. Many also prohibit foreigners from owning key natural resources like oil.
Ownership of something is frequently a grounds upon which to impose liability on a person based upon that ownership. For example, a car in an accident or real property where someone is injured.
I have never seen any US law that specifically restricts ownership,
and I suspect that there are none (possibly for constitutional
reasons). Is it a fact that there are no such laws? (If there are any
such laws, what interests me is whether "ownership" can be construed
as an "act").
There is nothing unconstitutional about such a law although if you owned something at the time that the law was enacted and had to give up ownership as a result of the law, you might be entitled to compensation under the 5th Amendment eminent domain provisions. There are many such laws, as noted above. You could call "ownership" an act in those circumstances, although the question seems to suggest that there is some constitutional or other requirement that laws only prohibit "acts" and that is not the case. Laws make likewise prohibit inaction, although they do so less often.
