can i be kept out of businesses? Property Invasion, Damages, Trespass

Nebraska

My abusive x boyfriend owns the land and buildings of a strip mall. He rents the bays to businesses. He sent me a letter that says if I go in any of them I will be immediately arrested for trespassing. I have never been to some of them nor have I ever caused any problems there.
My lawyer told me that he does not think it is legal for him to keep me out of those businesses. It would be up to the owners of the businesses.
Sat I went into a bar there and the owner of the bar asked me and my coworkers to leave. I said okay and polietly left. The next morning I got a call from the small town police there that said they were trying to get a warrant for my arrest for trespassing.
Can he do this to me?