Symmetric approximation of frames and bases in Hilbert spaces

Frank, Michael; Paulsen, Vern; Tiballi, Terry

doi:10.1090/S0002-9947-01-02838-0

Symmetric approximation of frames and bases in Hilbert spaces
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by Michael Frank, Vern I. Paulsen and Terry R. Tiballi PDF

Trans. Amer. Math. Soc. 354 (2002), 777-793 Request permission

Abstract:

We introduce the symmetric approximation of frames by normalized tight frames extending the concept of the symmetric orthogonalization of bases by orthonormal bases in Hilbert spaces. We prove existence and uniqueness results for the symmetric approximation of frames by normalized tight frames. Even in the case of the symmetric orthogonalization of bases, our techniques and results are new. A crucial role is played by whether or not a certain operator related to the initial frame or basis is Hilbert-Schmidt.

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