Journal of Function Spaces

Journal of Function Spaces / 2004 / Article

Open Access

Volume 2 |Article ID 814683 | https://doi.org/10.1155/2004/814683

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

Academic Editor: Sten Kaijser
Received01 Mar 2003

Abstract

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+t1)K2(t,f;H¯)2dρ(t))1/2 with some positive Radon measure ρ on the compactified half-line [0,]. The result was re-proved in [1] in the finite-dimensional case. The purpose of this note is to extend the proof given in [1] to cover the infinite-dimensional case. Moreover, the presentation of the aforementioned proof in [1] 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.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views88
Downloads396
Citations

Related articles

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.