International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 468907 | https://doi.org/10.1155/S0161171203202349

James R. Holub, "Riesz bases and positive operators on Hilbert space", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 468907, 2 pages, 2003. https://doi.org/10.1155/S0161171203202349

Riesz bases and positive operators on Hilbert space

Received02 Feb 2002

Abstract

It 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 on H in which it is an orthonormal basis, thereby extending the sense in which Riesz bases and orthonormal bases are thought of as being the same. A consequence of the method of proof of this result yields a series representation for all positive isomorphisms on a Hilbert space.

Copyright © 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.


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