Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations

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dc.creatorCasazza, Peter G.
dc.date1998-11-24
dc.date.accessioned2026-07-07T05:26:59Z
dc.date.available2026-07-07T05:26:59Z
dc.descriptionWe show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included which shows that this is best possible in that: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.
dc.descriptionto appear: J. of Fourier Anal. and Appl's
dc.identifierhttps://arxiv.org/abs/math/9811148
dc.identifierhttp://arxiv.org/abs/math/9811148
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77760
dc.subjectFunctional Analysis
dc.subject46B20; 46C05
dc.titleEvery frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
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