Suppose that the manager uses as an argument something as vague as "I didn't like what you did here last week" and does not cite any law nor policy.
Absolutely. The person having control other the establishment can disallow you to enter unless the reason is illegal discrimination. They don’t need to cite any law, “I don’t want you in here” is enough reason. No explanation needed why and if they give an explanation, “I don’t like your face” is enough.