Controlled K-g-Frames in Hilbert Spaces

Hua, Dingli; Huang, Yongdong

doi:10.1007/s00025-016-0613-0

Cited by 17 publications

(11 citation statements)

References 16 publications

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“…Since then, controlled frames have been widely studied. In 2016, Hua and Huang [23] introduced (C, C ′ )-controlled K-g-frame as follows: Assume that K, C, C ′ be linear and bounded operators on H such that C and C ′ are positive and have bounded inverse. The family {Λ j :…”

Section: Controlled Framesmentioning

confidence: 99%

Controlled weaving frames in Hilbert spaces

Rezapour

Rahimi

Osgooei

et al. 2019

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled weaving K-g-frames is given in terms of an operator. Finally, we show that if bounds of frames associated with atomic spaces are positively confined, then controlled K-g-woven frames gives ordinary weaving K-frames and vice-versa.

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Section: Controlled Framesmentioning

confidence: 99%

Controlled weaving frames in Hilbert spaces

Rezapour

Rahimi

Osgooei

et al. 2019

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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“…Controlled frames in Hilbert C * -modules was introduced by Kouchi and Rahimi [14], where the authors showed that they share many useful properties with their corresponding notions in a Hilbert space. Finally, we note that controlled K-g-frames in Hilbet spaces have been introduced by Hua and Huang [15]. The theory of continuous frames has been generalized in Hilbert C * -modules.…”

Section: Introductionmentioning

confidence: 99%

Controlled Continuous $$ - $K$ - $g$ -Frames for Hilbert $C^{}$ -Modules

Touri

Labrigui

Rossafi

et al. 2021

Abstract and Applied Analysis

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Frame theory has a great revolution for recent years. This theory has been extended from Hilbert spaces to Hilbert C ∗ -modules. In this paper, we define and study the new concept of controlled continuous ∗ - K - g -frames for Hilbert C ∗ -modules and we establish some properties.

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“…Recently, controlled frames have been presented by Balazs and et al in [1] to improve the numerical efficiency of interactive algorithms for inverting the frame operator on Hilbert spaces. After, controlled frames have been studied for another kind of frames in [14,16,17,18]. This manuscript is organized as follows: In Section 2, we study a new identity for the eigenvalues of the controlled frame operator and review the notation of controlled fusion frames with some results about these operators.…”

Section: Introductionmentioning

confidence: 99%

Robustness of controlled fusion frames under erasures of subspaces and the approximation operator

Ahmadi,

Rahimlou,

Sadri

2021

Preprint

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Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical wavelets. In this note, we aim to study some new results about controlled fusion frames and behavior of them under erasures. Finally, we will introduce the approximation operator for these frames and a result of the composition of the operators of two controlled fusion frames will be proved.

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Controlled K-g-Frames in Hilbert Spaces

Cited by 17 publications

References 16 publications

Controlled weaving frames in Hilbert spaces

Controlled weaving frames in Hilbert spaces

Controlled Continuous $$ - $K$ - $g$ -Frames for Hilbert $C^{}$ -Modules

Robustness of controlled fusion frames under erasures of subspaces and the approximation operator

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Controlled K-g-Frames in Hilbert Spaces

Cited by 17 publications

References 16 publications

Controlled weaving frames in Hilbert spaces

Controlled weaving frames in Hilbert spaces

Controlled Continuous∗-K-g-Frames for HilbertC∗-Modules

Robustness of controlled fusion frames under erasures of subspaces and the approximation operator

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Controlled Continuous $$ - $K$ - $g$ -Frames for Hilbert $C^{}$ -Modules