Yacin Ameur, "A new proof of Donoghue's interpolation theorem", Journal of Function Spaces, vol. 2, Article ID 814683, 13 pages, 2004. https://doi.org/10.1155/2004/814683
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 to be exact interpolation with respect to a regular Hilbert couple it is necessary and sufficient that the norm in be representable in the form with some positive Radon measure on the compactified half-line . The result was re-proved in  in the finite-dimensional case. The purpose of this note is to extend the proof given in  to cover the infinite-dimensional case. Moreover, the presentation of the aforementioned proof in  was slightly flawed, because we forgot to include a reference to ‘Donoghue's Lemma’, which is implicitly used in the proof. Hence we take this opportunity to correct that flaw.
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