Operator is a poorly defined word. In some cases it is very easy to establish who the operator is.
For example, Mike's BA example, some division within BA (or possibly the main holding company) has an Air Operators Certificate and the referenced aircraft are operated under this certificate. Hence the issue of who the operator is crystal clear.
Equally, in Pace's case (a professional pilot flying on behalf of and at the instruction of the aircraft owner and not responsible for maintenance in anyway beyond the normal PIC responsibilities) it should be very clear that Pace is not the operator, 'just' the PIC/Commander.
What is much less clear in this case is who would be deemed to be the operator.
Hypothetical Case
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Say for example Pace works for Williams (a Woking based F1 team that races globally) and bases their Citation at EGLF. Say Williams has a subsidiary based in Delaware (to facilitate paying its highly paid staff offshore) and this subsidiary is the owner of the aircraft, coordinates the maintenance and receives dispatch requests from the rest of the Williams group.
Is the Operator the company that owns, flight plans, and despatches the plane, or the Group company that requested the dispatch, or the Holding company (which for the sake of argument is a Netherlands Antilles co for tax reasons) or some intermediate entity of EASA's choosing.
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Corporate jet operators are on the N for many reasons, and I doubt any of the reasons include helping pilots avoid sitting the IR exams! As such they will stay N and will either just tell their pilots to knuckle down or arrange a structure to avoid the problem. They will surely choose the option that is easier and cheaper from the owner's perspective.
EAl,
I am pretty sure the language is Member State (not EU, ECC, or anything else). I also believe it is a Member of EASA they are referencing. I note Norway, Iceland, and Switzerland appear to be EASA members but not part of the EU.