If there was no non-competition clause, then it is perfectly legal for him to open a competing business in the same building: anyone may open any business, in competition to anyone, when there is no non-competition agreement. However, you have the right to exclude the former employee from your premises or rental property: he has no right to come onto/into it if you don't give him permission. Tell him that he is not welcome: then the next time he comes, you can call the police because he is trespassing. You can also inform him that if he tries to scare away or harass your customers, you will sue him for tortious interference with economic advantage--i.e. for wrongfully interfering with your business. You could potentially get monetary compensation and/or a court order that he stop doing this.