The trustees may appoint one or more persons to constitute a police department for the headquarters and for each campus of the California State University. Persons employed and compensated as members of a California State University police department, when so appointed and duly sworn, are peace officers. However, such peace officers shall not exercise their powers or authority except (a) at the headquarters or upon any campus of the California State University and in an area within one mile of the exterior boundaries of each campus or the headquarters, and in or about other grounds or properties owned, operated, controlled, or administered by the California State University, or by trustees or the state on behalf of the California State University, and (b) as provided in Section 830.2 of the Penal Code.