## Symmetric approximation of frames and bases in Hilbert spaces

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- by Michael Frank, Vern I. Paulsen and Terry R. Tiballi
- Trans. Amer. Math. Soc.
**354**(2002), 777-793 - DOI: https://doi.org/10.1090/S0002-9947-01-02838-0
- Published electronically: August 31, 2001
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## 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.## References

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## Bibliographic Information

**Michael Frank**- Affiliation: Universität Leipzig, Mathematisches Institut, D–04109 Leipzig, F.R.Germany
- Email: frank@mathematik.uni-leipzig.de
**Vern I. Paulsen**- Affiliation: Department Mathematics, University of Houston, Houston, Texas 77204-3476
- MR Author ID: 137010
- ORCID: 0000-0002-2361-852X
- Email: vern@math.uh.edu
**Terry R. Tiballi**- Affiliation: Department Mathematics, SUNY at Oswego, Oswego, New York 13126
- Email: tiballi@oswego.edu
- Received by editor(s): December 14, 1998
- Received by editor(s) in revised form: August 1, 2000
- Published electronically: August 31, 2001
- Additional Notes: The first and second authors were supported in part by an NSF grant.
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 777-793 - MSC (2000): Primary 42C99; Secondary 46C05, 47B10, 65T99
- DOI: https://doi.org/10.1090/S0002-9947-01-02838-0
- MathSciNet review: 1862567