Oblique projections and frames

Antezana, J.; Corach, G.; Ruiz, M.; Stojanoff, D.

doi:10.1090/S0002-9939-05-08143-8

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.

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