Geometry of epimorphisms and frames

Corach, Gustavo; Pacheco, Miriam; Stojanoff, Demetrio

doi:10.1090/s0002-9939-04-07380-0

Cited by 9 publications

(12 citation statements)

References 20 publications

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“…△ Remark 4.3. This geometric presentation is similar to the presentation of vector frames done in [16]. The relationship is based on the following fact:…”

Section: General Reconstruction Systemsmentioning

confidence: 93%

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Duality in reconstruction systems

Massey

Ruiz

Stojanoff

2012

Linear Algebra and its Applications

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We consider the notion of finite dimensional reconstructions systems (RS's), which includes the fusion frames as projective RS's. We study erasures, some geometrical properties of these spaces, the spectral picture of the set of all dual systems of a fixed RS, the spectral picture of the set of RS operators for the projective systems with fixed weights and the structure of the minimizers of the joint potential in this setting. WeIn the case J = {j}, the lower bound in Theorem 3.3 is greater than that obtained in [3]:Proposition 3.4. Let V, and M J be as in Theorem 3.3, with J = {j}. ThenProof. We can suppose M −1 J ≥ 1, since otherwise (7) is evident. Note that1. The vector µ ∈ Λ(D(V)).1. The set Λ(OP v ) is convex.

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“…△ Remark 4.3. This geometric presentation is similar to the presentation of vector frames done in [16]. The relationship is based on the following fact:…”

Section: General Reconstruction Systemsmentioning

confidence: 93%

“…In [16] it is proved that these facts are sufficient to assure that RS is a smooth submanifold of L(m, k, d) (actually it is an open subset) such that the map π V : Gl (K) → RS becomes a smooth submersion. On the other hand, we can parametrize D(V) in two different ways :…”

Section: General Reconstruction Systemsmentioning

confidence: 99%

Duality in reconstruction systems

Massey

Ruiz

Stojanoff

2012

Linear Algebra and its Applications

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“…In fact, F ∈ E if and only if F F * ∈ GL(H); therefore, it is easy to check that F † = F * (F F * ) −1 , and this shows that, on E, F → F † is continuous (moreover, real analytic). About the topological properties of E, the reader is referred to [10]. Recall from [10]…”

Section: Frame Decompositions Of Oblique Projectionsmentioning

confidence: 99%

Sampling Formulae and Optimal Factorizations of Projections

Andruchow

Antezana

Corach

2008

STSIP

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Let H be a Hilbert space, W a closed subspace of H, and Q a (linear bounded) projection from H onto W with null space M ⊥ . We study decompositions like Qf = n∈N f, h n f n , where {f n } n∈N and {h n } n∈N are frames for the subspaces W and M, respectively. This type of decompositions corresponds to sampling formulae. By considering the synthesis operator F (resp. H) of the sequence {f n } n∈N (resp. {h n } n∈N ), the formula above can be expressed as the factorization Q = F H * . We study different properties of these factorizations and decompositions of oblique and orthogonal projections. Several characterizations of these decompositions are presented. By means of an operator inequality for positive operators, we get a result which minimizes the norm of F − H.

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“…Our next problem is motivated from the works of Dykema and Strawn in Hilbert spaces [15,23,58,66,97,[103][104][105] and Corach, Pacheco, and Stojanoff [53].…”

Section: Introductionmentioning

confidence: 99%

Feichtinger Conjectures, $R_\varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces

Krishna¹

2022

Preprint

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Motivated from two decades old famous Feichtinger conjectures for frames, R ε -conjecture and Weaver's conjecture for Hilbert spaces (and their solution by Marcus, Spielman, and Srivastava), we formulate Feichtinger conjectures for p-approximate Schauder frames, R ε -conjecture, Weaver's conjectures and Akemann-Weaver conjectures for Banach spaces. We also formulate conjectures on p-approximate Schauder frames based on the results of Casazza for frames for Hilbert spaces. We state conjectures and problems for p-approximate Schauder frames based on fundamental inequality for frames for Hilbert spaces and scaling problem for Hilbert space frames. Based on Kothe-Lorch theorem for Riesz bases for Hilbert spaces, we formulate a problem for p-approximate Riesz bases for Banach spaces. We formulate dynamical sampling problem for p-approximate Schauder frames for Banach spaces. We ask phase retrieval problem and norm retrieval problem for p-approximate Schauder frames for Banach spaces. We also formulate discretization problem for continuous p-approximate Schauder frames.

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Geometry of epimorphisms and frames

Cited by 9 publications

References 20 publications

Duality in reconstruction systems

Duality in reconstruction systems

Sampling Formulae and Optimal Factorizations of Projections

Feichtinger Conjectures, $R_\varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces

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