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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Oblique projections and frames


Authors: J. Antezana, G. Corach, M. Ruiz and D. Stojanoff
Journal: Proc. Amer. Math. Soc. 134 (2006), 1031-1037
MSC (2000): Primary 42C15, 47A05
Published electronically: November 7, 2005
MathSciNet review: 2196035
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08143-8
PII: S 0002-9939(05)08143-8
Keywords: Frames, oblique projections
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.