Multipliers for von Neumann–Schatten Bessel sequences in separable Banach spaces

Javanshiri, Hossein; Choubin, Mehdi

doi:10.1016/j.laa.2018.01.029

Cited by 8 publications

(5 citation statements)

References 48 publications

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“…Since their introduction in 2007 (see [4]), ordinary Bessel multipliers, as a generalization of Gabor multipliers [12], have been extensively generalized and studied, see for example [3,5,17,18,24]. The reader will remark that invertible Bessel multipliers is a proper generalization of duality notion in Hilbert spaces which permits us to have different reconstruction strategies.…”

Section: Resultsmentioning

confidence: 99%

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Javanshiri¹,

Fattahi²,

Sargazi³

2018

Preprint

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To achieve our main research goal, first we survey the approaches towards dual fusion frames existing in the literature and agree on the notion of duality for fusion frames in the sense of Kutyniok, Paternostro and Philipp (Oper. Matrices 11 (2017), no. 2, 301-336). As a main result we show that different fusion frames have different dual fusion frames. Moreover, this duality notion leads to a new definition of Bessel fusion multipliers which is a slightly modified version of the commonly used definitions. Particularly, we show that with this definition in many cases Bessel fusion multipliers behave similar to ordinary Bessel multipliers. Finally, special attention is devoted to the study of dual fusion frames induced by an invertible Bessel fusion multiplier.

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Section: Resultsmentioning

confidence: 99%

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Javanshiri¹,

Fattahi²,

Sargazi³

2018

Preprint

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“…which has been studied by Rahimi [12] and in a much more general setting by Javanshiri and Choubin in [9], where, here, and in the sequel ℓ ∞ (I) has its usual meanings.…”

Section: Preliminariesmentioning

confidence: 99%

“…The notions Fourier and Gabor multipliers were extended to ordinary Bessel multipliers in Hilbert spaces by Balazs [2], p-Bessel sequences in Banach spaces by Balazs and Rahimi in [13], von Neumann-Schatten setting [9] and continuous setting in [3]. In [14], sufficient and/or necessary conditions for invertibility of ordinary Bessel multipliers have determined depending on the properties of the analysis and synthesis sequences, as well as the symbol.…”

Section: Introductionmentioning

confidence: 99%

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Invertibility of generalized g-frame multipliers in Hilbert spaces

Abolghasemi¹,

Tolooei²,

Moosavianfard³

2019

Preprint

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In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame multiplier. Also we give several approaches for constructing invertible generalized g-frame multipliers from the given one. It is worth mentioning that some of our results are quite different from those studied in the previous literatures on this topic. 2010 MSC : 42C15, 47A05, 41A58.

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“…A number of variations and generalizations of duality notion can be found in Li and Ogawa 2,3 in the more general context of pseudo-duality, atomic system for subspace, 4,5 approximate duality, 6,7 and generalized duality. [7][8][9] In many situations, it is important to know which properties of frames are stable if we slightly modify the elements of the systems. This gives rise to the so-called perturbation theory.…”

Section: Introductionmentioning

confidence: 99%

The effect of perturbations of frames on their alternate and approximately dual frames

Javanshiri

Hajiabootorabi

Mardanbeigi

2021

Math Methods in App Sciences

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Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory, and sensor modeling. In recent years, the computing of the associated deviations of the canonical and alternate dual frames from the original ones has been considered by functional analysts. In this paper, we consider the quantitative measurement of the associated deviations of the alternate and approximately dual frames from the original ones. More precisely, it is proved that if the sequence Ψ is sufficiently close to the frame Φ, then for given approximately dual frame Φ ad of Φ, the approximately dual frame Ψ ad of Ψ can be found which is close to Φ ad , and particularly, we estimate their deviation in terms of the distance of the operators  1 ∶= T Φ U Φ ad and  2 ∶= T Ψ U Ψ ad and their approximation rates, where T X and U X denote the synthesis and analysis operators of the frame X, respectively. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic.

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Multipliers for von Neumann–Schatten Bessel sequences in separable Banach spaces

Cited by 8 publications

References 48 publications

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers

Invertibility of generalized g-frame multipliers in Hilbert spaces

The effect of perturbations of frames on their alternate and approximately dual frames

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