Legal Question in Business Law in California

It is common for businesses to negotiate terms of a lease prohibiting or limiting competing tenants in the same retail facility, but unless one or both leases has such a provision, there is nothing illegal about it.

Yes, it is legal, although many, perhaps most, shopping centers use leases that guarantee a tenant exclusive rights to conduct a type of business in that center, and/or forbid a tenant to compete with another existing tenant. Such leases are considered perfectly legal and often necessary to promote the success of the first bakery, sporting-goods store, pizzeria, etc. to arrive at the shopping center.