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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Symmetric approximation of frames and bases in Hilbert spaces


Authors: Michael Frank, Vern I. Paulsen and Terry R. Tiballi
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
Published electronically: August 31, 2001
MathSciNet review: 1862567
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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.


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Additional 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
Email: vern@math.uh.edu

Terry R. Tiballi
Affiliation: Department Mathematics, SUNY at Oswego, Oswego, New York 13126
Email: tiballi@oswego.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02838-0
Keywords: Hilbert space, Riesz basis, frame, symmetric orthogonalization, symmetric approximation, Hilbert-Schmidt operator
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.
Article copyright: © Copyright 2001 American Mathematical Society