What is a Monopoly?

In some circumstances, preventing a competitor from entering a market could be considered an antitrust violation, but this is not one of them.  Do you have a lease or other contract with the market which gives you the right to utilize its space?  If so, what does the lease provide?  Absent a contractual right, or discrimination on a prohibited basis (race, gender, etc.), or some zoning issue, a landlord  has the right to lease its space, or not lease its space, to whatever tenants it wishes.  It is not uncommon for tenants to protect their rights with restrictive covenants in their leases which prohibit the landlord from renting space in the particular shopping center or market to a competitor.  Although your competitor may not have such a restrictive covenant which mandates that the landlord keep you out, if the landlord agrees to keep you out, it has the right to do so.