Aispace is separated in sectors, and each one has its own frequency. What's the airspace capacity for procedural and radar services, for a single sector?
There's probably not a specific number. The answer will probably end up being "however many can do and maintain separation." Some sectors will include more complex maneuvering (more than one airport, several different approaches, both commercial and GA aircraft) so the airspace would have to be broken up into many smaller sectors with fewer aircraft in each to reduce workload. Whereas if you're talking about en-route, where the aircraft are not doing a lot of maneuvering the controller can probably deal with several times as many planes. If you think of arrivals at a busy airport, the airspace is broken into several different controllers, whereas often one guy in the tower is doing all of the landing clearances. That means he controls every single inbound flight whereas the approach controller is only juggling the portion that approach through his airspace. The workload per plane for the tower on landing is much lower since the approach controller will pass aircraft to him to him separated and already on ILS or with a visual on the runway. So all he is responsidle for is is making sure the runway is clear for each landing. In most situations tower only talks to the arrivals twice. Once to give clearance and then to pass them on to ground.
As already mentioned, airspace capacity is not a simple term. One very important aspect is aircraft separation. For example in procedural control separation is time based and (if I recall) it's 10 minutes flight time. That's definitely less capacity when compared to 10 miles for en-route and 6 for approach.
One other important aspect for calculating the capacity of a sector is the workload. Workload includes the time a controller spends talking (and listenign) to aircraft, coordinating flights, how much time is left for thinking and resolving conflicts etc. Eurocontrol has developed the CAPAN (capacity analyzer) methodology for calculating capacity.
Each sector is unique and has a unique capacity which the ANSP managing the sector should calculate. There is no "one size fits all" solution.