Riesz bases and positive operators on Hilbert space

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2003-01-01
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Hindawi
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 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.

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Citation
James 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/S0161171203202349