This paper presents an initial implementation of an autonomous Urban Air Mobility network management and aircraft separation service for urban airspace that does 1) departure and arrival scheduling across the network, 2) continuous trajectory management to ensure safe separation between aircraft, and 3) seamless integration with traditional operations. The highly-autonomous AutoResolver algorithm developed for traditional aviation was extended to provide these capabilities. An evaluation of this initial implementation was conducted in fast-time simulations using a dense, two-hour traffic scenario with Urban Air Mobility aircraft flying between a network of 20 vertiports in the Dallas-Fort Worth metroplex. When the spatial separation was reduced from 0.3nmi to 0.1nmi, the total delay decreased by 7.3%; when the temporal separation was reduced from 60s to 45s, the total delay decreased by 28.4%. The total number of conflict resolutions decreased by 26% and 17%, respectively. Furthermore, when a scheduling horizon greater than the duration of UAM flights was used (50min), most conflicts were resolved pre-departure producing ground delay. By comparison, when a shorter scheduling horizon was used (8min), most conflicts were resolved post-departure generating airborne delay. For all scheduling and separation constraints tested, AutoResolver prevented loss of separation from occurring. Urban Air Mobility operations have the ability to revolutionize how people and goods are transported and this paper presents initial research focusing on the high levels of autonomy required for an airspace system capable of scaling to handle significantly higher densities of aircraft.