A new proof of Donoghue's interpolation theorem

We give a new proof and new interpretation of Donoghue's interpolation theorem; for an intermediate Hilbert space H∗ to be exact interpolation with respect to a regular Hilbert couple H¯ it is necessary and sufficient that the norm in H∗ be representable in the form ‖f‖∗=(∫[0,∞](1