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
It is shown that a normalized Riesz basis for a Hilbert space (i.e., the isomorphic image of an orthonormal basis in ) induces in a natural way a new, but equivalent, inner product on 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.
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