Portraits and perturbations of Hilbert-Schmidt frame sequences (Q2091152)
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scientific article; zbMATH DE number 7610167
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Portraits and perturbations of Hilbert-Schmidt frame sequences |
scientific article; zbMATH DE number 7610167 |
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Portraits and perturbations of Hilbert-Schmidt frame sequences (English)
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31 October 2022
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The authors study perturbations in Hilbert-Schmidt frames (HS-frame). They prove that an arbitrary bounded invertible operator on \(l^2(J)\) transforms a HS-frame into another HS-frame and also present a sufficient condition on bounded operators on \(l^2(J)\) which transform an \(l^2(J)\)-decomposable HS-frame into another HS-frame (HS-Riesz basis, HS-frame sequence and HS-Riesz sequence). They further prove that suitably perturbing a HS-frame sequence (HS-Riesz sequence) leaves a HS-frame sequence (HS-Riesz sequence).
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frame
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HS-frame
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HS-frame sequence
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HS-Riesz basis
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HS-Riesz sequence
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