Some Properties of K-Frames in Quaternionic Hilbert Spaces

Ellouz, Hanen

doi:10.1007/s11785-019-00964-5

Cited by 8 publications

(2 citation statements)

References 18 publications

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“…Note that both real field and complex field are associative and commutative, while quaternion field only constitutes a non-commutative associative algebra, this key characteristic greatly limited mathematicians to establish a complete theory of functional analysis in Q-Hilbert spaces [14,15], which affected the development of quantum physics in Q-Hilbert space. Luckily, the study on quaternion field has been developed from the mathematical point of view, especially frames in Q-Hilbert space have been obtained some achievements in recent years [16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Duality and Sum on frames in Q-Hilbert spaces

2023

Preprint

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Quaternionic Hilbert space has received great attention in the research of quantum physics. The duality and sum of frames are hot issues in frame theory.In this paper,We firstly introduce the notion of pre-frame operators on frames in Q-Hilbert spaces, and characterize Hilbert(orthonormal) bases,frames, dual frames and Riesz bases, and obtain the accurate expressions of all dual frames of a given frame by taking advantage of pre-frame operators.We also characterize the dual frames through an operator equation. Secondly,we discuss sums of frames with the help of the pre-frame operators, and gain some more general methods to construct new frames. Moreover, we obtain a necessary and sufficient condition for the finite sum of frames to be a (tight) frame.

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Section: Introductionmentioning

confidence: 99%

Duality and Sum on frames in Q-Hilbert spaces

2023

Preprint

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“…Muraleetharan and Thirulogasanthar [19] studied the invariance of the Fredholm index under small norm operator and compact operator perturbations and with the association of the Fredholm operators, developed the theory of essential S-spectrum. K-frames in quaternionic Hilbert spaces were studied in [13]. Very recently, Sharma, Jarrah and Kaushik [24] introduced frame of operators in quaternionic Hilbert spaces and proved that they generalizes various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion frames) in separable quaternionic Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Trace class operators via OPV-frames

Bhardwaj

Sharma

Kaushik

2021

Filomat

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Trace class operators for quaternionic Hilbert spaces (QHS) were studied by Moretti and Oppio [18]. In this paper, we study trace class operators via operator valued frames (OPV-frames). We introduce OPV-frames in a right quaternionic Hilbert space H with range in a two sided quaternionic Hilbert space K and obtain various results including several characterizations of OPV-frames. Also, we obtain a necessary and sufficient condition for a bounded operator on a right QHS to be a trace class operator which generalizes a similar result by Attal [2]. Moreover, we construct a trace class operator on a two sided QHS. Finally, we study quaternionic quantum channels as completely positive trace preserving maps and obtain various Choi-Kraus type representations of quaternionic quantum channels using OPV-frames in quaternionic Hilbert spaces.

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Dual and canonical dual K-Bessel sequences in quaternionic Hilbert spaces

Ellouz

2021

RACSAM

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Some Properties of K-Frames in Quaternionic Hilbert Spaces

Cited by 8 publications

References 18 publications

Duality and Sum on frames in Q-Hilbert spaces

Duality and Sum on frames in Q-Hilbert spaces

Trace class operators via OPV-frames

Dual and canonical dual K-Bessel sequences in quaternionic Hilbert spaces

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