Holub, James R.2017-09-182017-09-182003-01-01James R. Holub, “Riesz bases and positive operators on Hilbert space,” International Journal of Mathematics and Mathematical Sciences, vol. 2003, no. 18, pp. 1173-1174, 2003. doi:10.1155/S0161171203202349http://hdl.handle.net/10919/79094It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product onH in which it is an orthonormal basis, thereby extending thesense in which Riesz bases and orthonormal bases are thought ofas being the same. A consequence of themethod of proof of this result yields a series representation forall positive isomorphisms on a Hilbert space.application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereed2017-09-18Copyright © 2003 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.https://doi.org/10.1155/S0161171203202349