Oblique projections and frames
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- by J. Antezana, G. Corach, M. Ruiz and D. Stojanoff PDF
- Proc. Amer. Math. Soc. 134 (2006), 1031-1037 Request permission
Abstract:
We characterize those frames on a Hilbert space $\mathcal {H}$ which can be represented as the image of an orthonormal basis by an oblique projection defined on an extension $\mathcal {K}$ of $\mathcal {H}$. We show that all frames with infinite excess and frame bounds $1\le A \le B$ are of this type. This gives a generalization of a result of Han and Larson which only holds for normalized tight frames.References
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Additional Information
- J. Antezana
- Affiliation: IAM-CONICET and Departamento de Matemática, FCE-UNLP, La Plata, Argentina
- Email: antezana@mate.unlp.edu.ar
- G. Corach
- Affiliation: IAM-CONICET and Departamento de Matemática, FI-UBA, Saavedra 15, Piso 3 (1083), Ciudad Autónoma de Buenos Aires, Argentina
- Email: gcorach@fi.uba.ar
- M. Ruiz
- Affiliation: IAM-CONICET and Departamento de Matemática, FCE-UNLP, La Plata, Argentina
- Email: mruiz@mate.unlp.edu.ar
- D. Stojanoff
- Affiliation: IAM-CONICET and Departamento de Matemática, FCE-UNLP, La Plata, Argentina
- Email: demetrio@mate.unlp.edu.ar
- Received by editor(s): September 22, 2004
- Published electronically: November 7, 2005
- Additional Notes: This research was partially supported by CONICET (PIP 2083/00), UBACYT I030, UNLP (11 X350) and ANPCYT (PICT03-9521)
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1031-1037
- MSC (2000): Primary 42C15, 47A05
- DOI: https://doi.org/10.1090/S0002-9939-05-08143-8
- MathSciNet review: 2196035