Frames for Operators in Banach Spaces

Ramu, G.; Johnson, P. Sam

doi:10.1007/s40306-017-0210-7

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…Poumai and Jahan [30] introduced atomic systems for operators in Banach spaces. Frames for operators in Banach spaces were further studied in [8,18]. Outline of the paper.…”

Section: Introductionmentioning

confidence: 99%

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Approximative K-atomic decompositions and frames in Banach spaces

Jahan

2018

AJMS

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K-frames and atomic systems for an operator K in Hilbert spaces were introduced by Gavruta [17] and further studied by Xio, Zhu and Gavruta [35]. In this paper, we have introduced the notion of an approximative atomic system for an operator K in Banach spaces and obtained interesting results. A complete characterization of family of approximative local atoms of subspace of Banach space has been obtained. Also, a necessary and sufficient condition for the existence of an approximative atomic system for an operator K is given. Finally, explicit methods are given for the construction of an approximative atomic systems for an operator K from a given Bessel sequence and approximative X d -Bessel sequence.∞ k=1 f, f k f k , f ∈ H. The frame operator S is bounded, linear and invertible on H. Thus, a frame for H allows each vector in H to be written as a linear combination of the elements in the frame, but the linear independence between the elements is not required; i.e for each vector f ∈ H we have,

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“…Poumai and Jahan [30] introduced atomic systems for operators in Banach spaces. Frames for operators in Banach spaces were further studied in [8,18]. Outline of the paper.…”

Section: Introductionmentioning

confidence: 99%

“…Gavruta [15], introduced and studied atomic system for an operator K and the notion of K-frame in a Hilbert space, see also [16]. Frames for operators in Banach spaces were further studied in [8,17,25]. Xiao et al [32] discussed relationship between K-frames and ordinary frames in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Approximative K-atomic decompositions and frames in Banach spaces

Jahan

2018

AJMS

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“…In the literature there are many further studies or variations of K-frames (see for example [23,25,28,31,32,35] and the references therein).…”

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confidence: 99%

Frames and weak frames for unbounded operators

Bellomonte

Corso

2020

Adv Comput Math

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Few years ago Gȃvruţa gave the notions of K-frame and atomic system for a linear bounded operator K in a Hilbert space H in order to decompose R(K), the range of K, with a frame-like expansion. These notions are here generalized to the case of a densely defined and possibly unbounded operator on a Hilbert space A in a continuous setting, thus extending what have been done in a previous paper in a discrete framework.

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VON NEUMANN–SCHATTEN p-FRAMES FOR OPERATORS

Takhteh,

Mirzaee Azandaryani

2024

Rocky Mountain J. Math.

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Frames for Operators in Banach Spaces

Cited by 3 publications

References 14 publications

Approximative K-atomic decompositions and frames in Banach spaces

Approximative K-atomic decompositions and frames in Banach spaces

Frames and weak frames for unbounded operators

VON NEUMANN–SCHATTEN p-FRAMES FOR OPERATORS

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