Is this shielded loop antenna balanced?
Easiest to understand in transmission mode. Consider currents in the feeding transmission line are separated into differential and common mode components. The differential currents are equal in magnitude but flow in opposite directions in the core wire and shield. The common mode components both flow the same way in core and shield. Any pattern of current can be separated into such components.
When they emerge from the open end of the coax, the common mode currents flow out and head in opposite directions round the loop. Any magnetic field induced through the loop by the current flow in one direction is cancelled by that flowing in the opposite direction.
On the other hand, differential currents in the core and shield are flowing in opposite directions and hence result in current circulating around the loop. This will induce a magnetic field through the loop. If the currents oscillate, the loop will radiate.