Riesz bases and positive operators on Hilbert space
Holub, James R.
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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.