Some constructions of $K$-frames and their duals

Neyshaburi, Fahimeh Arabyani; Arefijamaal, Ali Akbar

doi:10.1216/rmj-2017-47-6-1749

Cited by 30 publications

(26 citation statements)

References 14 publications

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“…Let Λ j f := f, e j e j = f j e j , where f = (f 1 , f 2 , f 3 ) and j = 1, 2, 3. It is clear that (W j , Λ j , 1) is a K-g-fusion frame for H with bounds 1 2 and 1, respectively. Assume that (W j , Λ j , 1) is a U -g-fusion frame for H. Then, by Proposition 1, there exists A > 0 such that KK * ≥ AU U * .…”

Section: K-g-fusion Framesmentioning

confidence: 99%

Constructions of K-g-fusion and their dual in Hilbert spaces

Ahmadi¹,

Rahimlou²,

Sadri³

et al. 2020

MIF

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Frames for operators or K-frames were recently considered by Gȃvruţa (2012) in connection with atomic systems. Also, generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators also known as K-g-fusion frames and we get some results for characterization of these frames. We further discuss dual and Q-dual in connection with K-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct K-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for K-g-fusion frames.

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Section: K-g-fusion Framesmentioning

confidence: 99%

Constructions of K-g-fusion and their dual in Hilbert spaces

Ahmadi¹,

Rahimlou²,

Sadri³

et al. 2020

MIF

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“…where K † is the pseudoinverse of K . For further information in K -frames refer to [1,19,25]. Suppose {f i } i∈I is a Bessel sequence.…”

Section: K -Framesmentioning

confidence: 99%

“…An approach to the K -duals of a K -frame can be found in [1]. Notice that K -duals of [1] satisfy (2.3).…”

Section: R(k) ⊆ R(t F )mentioning

confidence: 99%

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Some Results of K-Frames and Their Multipliers

2020

Turk J Math

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“…When working on atomic systems for operators, Gȃvruţa [12] put forward the concept of -frames for a given linear bounded operator , which allows atomic decomposition of elements from the range of and, in general, the range may not be closed. Moreover, it has been shown in [13][14][15][16] that in many ways -frames behave completely differently from frames, although a -frame is a generalization of a frame; see also [17,18].…”

Section: Introductionmentioning

confidence: 99%

Some Properties of Canonical Dual K-Bessel Sequences for Parseval K-Frames

Xiang

2019

Journal of Function Spaces

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The concept of canonical dual -Bessel sequences was recently introduced, a deep study of which is helpful in further developing and enriching the duality theory of -frames. In this paper we pay attention to investigating the structure of the canonical dual -Bessel sequence of a Parseval -frame and some derived properties. We present the exact form of the canonical dual -Bessel sequence of a Parseval -frame, and a necessary and sufficient condition for a dual -Bessel sequence of a given Parsevalframe to be the canonical dual -Bessel sequence is investigated. We also give a necessary and sufficient condition for a Parseval -frame to have a unique dual -Bessel sequence and equivalently characterize the condition under which the canonical dual -Bessel sequence of a Parseval -frame admits a unique dual * -Bessel sequence. Finally, we obtain a minimal norm property on expansion coefficients of elements in the range of resulting from the canonical dual -Bessel sequence of a Parseval -frame.

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Some constructions of $K$-frames and their duals

Cited by 30 publications

References 14 publications

Constructions of K-g-fusion and their dual in Hilbert spaces

Constructions of K-g-fusion and their dual in Hilbert spaces

Some Results of K-Frames and Their Multipliers

Some Properties of Canonical Dual K-Bessel Sequences for Parseval K-Frames

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