Strongly irreducible factorization of quaternionic operators and Riesz decomposition theorem

Pamula, Santhosh Kumar

doi:10.1007/s43037-020-00084-9

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…First and foremost, we have by [4,Theorem 4.4] σ S (T ) = σ S (T 1 ) ∪ σ S (T 2 ) Take σ 1 = σ S (T 1 ) and σ 2 = σ S (T 2 ) and assume that dist(σ 1 , σ 2 ) > 0. According to the proof of [32,Theorem 6], there exist a pair of a non-empty disjoint axially symmetric domains (U σ 1 , U σ 2 ) such that…”

Section: Therefore (3)mentioning

confidence: 99%

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Riesz projection and essential $S$-spectrum in quaternionic setting

Baloudi¹,

Belgacem²,

Jeribi³

2021

Preprint

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This paper is devoted to the investigation of the Weyl and the essential S−spectra of a bounded right quaternionic linear operator in a right quaternionic Hilbert space. Using the quaternionic Riesz projection, the S−eigenvalue of finite type is both introduced and studied.In particular, we have shown that the Weyl and the essential S−spectra do not contain eigenvalues of finite type. We have also described the boundary of the Weyl S−spectrum and the particular case of the spectral theorem of the essential S−spectrum. Contents 1. Introduction 1 2. Mathematical preliminaries 3 2.1. Quaternions 3 2.2. Right quaternionic Hilbert space and operator 4 2.3. The quaternionic functional calculus 7 3. Riesz projection and essential spectrum 9 4. Some results on the Weyl S-spectrum 18 References 22

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Section: Therefore (3)mentioning

confidence: 99%

“…The technique of the proof is inspired from [4]. We also discuss the Riesz decomposition theorem [32,Theorem 6] in quaternionic setting. More precisely, we prove that this decomposition is unique.…”

Section: Introductionmentioning

confidence: 99%

Riesz projection and essential $S$-spectrum in quaternionic setting

Baloudi¹,

Belgacem²,

Jeribi³

2021

Preprint

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“…Let P [q] denote the corresponding Riesz projector with rang and kernel denoted by R(P [q] ) and N(P [q] ), respectively. Thanks to the Riesz decomposition theorem [34,Theorem 6] in quaternionic setting, we have…”

Section: Introductionmentioning

confidence: 99%

Riesz Projection and Essential S-spectrum in Quaternionic Setting

Baloudi

Belgacem

Jeribi

2022

Complex Anal. Oper. Theory

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This paper is devoted to the study of the S-eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the S-spectrum. Furthermore, we introduce the left and right Browder Sresolvent operators. Inspired by the S-resolvent equation, we give the Browder's S-resolvent equation in quaternionic setting. Contents 1. Introduction 1 2. Mathematical preliminaries 4 2.1. Quaternions 4 2.2. Operators acting on right quaternionic Hilbert space 5 2.3. The quaternionic functional calculus 6 3. Eigenvalue of finite type 9 4. Browder S-resolvent equation in quaternionic setting 17 References 22

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