Frobenius–Schur Factorization for Multivalued $${\varvec{2\times 2}}$$ 2 × 2 Matrices Linear Operator

Ammar, Aymen; Jeribi, Aref; Saadaoui, Bilel

doi:10.1007/s00009-016-0825-2

Cited by 18 publications

(2 citation statements)

References 25 publications

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“…They investigated some properties of the spectral theory of the matrix of multivalued linear operators. In [4], Ammar et al defined a new concept for 2×2 block matrix relations in Banach spaces. It was demonstrated that under some conditions on its inputs, this block is closed.…”

Section: The Set T Is Defined Bymentioning

confidence: 99%

A Characterization of the Essential Spectra of $$2\times 2$$ Block Matrices of Linear Relations

Ammar

Ezzadam

Jeribi

2021

Bull. Iran. Math. Soc.

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The main goal of this paper is to elaborate some results on the spectral properties of 2 × 2 block matrix linear relations with unbounded entries and with a domain consisting of vectors which satisfy certain relations between their components. We present some conditions to prove some Frobenius-Schur decompositions for linear relations and characterize the stability of the essential spectra of these linear relations. Our results generalize many known ones in the literature, in particular those obtained by Álvarez et al.

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Section: The Set T Is Defined Bymentioning

confidence: 99%

A Characterization of the Essential Spectra of $$2\times 2$$ Block Matrices of Linear Relations

Ammar

Ezzadam

Jeribi

2021

Bull. Iran. Math. Soc.

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“…Linear selections have been investigated in R. W. Cross [31] and have found several applications. In [26,27] A. Ammar, A. Jeribi and B. Saadaoui introduced the phenomenon of linear selection to ensure certain matrix decomposition (example: the Frobenius-Schur decomposition for multivalued matrices operator). The development of spectral theory for linear relations was the aim of recent paper in 2012 D. Gheorghe and F.-H. Vasilescu [35].…”

Section: Introductionmentioning

confidence: 99%

Demicompactness, selection of linear relation and application to multivalued matrix

Ammar

Jeribi

Saadaoui

2022

Filomat

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In this paper, we investigate the concept of demicompactness and we establish some new results in Fredholm theory connected with the existence of selections of a given linear relation and we explore the possibility of finding a selection demicompact for some linear relation demicompact. Moreover, we give the relationship of the resolvent set between the linear relation with its selection. Furthermore, we give an application to matrix linear relation.

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Basic Notations and Results

Jeribi

2021

Perturbation Theory for Linear Operators

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Frobenius–Schur Factorization for Multivalued $${\varvec{2\times 2}}$$ 2 × 2 Matrices Linear Operator

Cited by 18 publications

References 25 publications

A Characterization of the Essential Spectra of $$2\times 2$$ Block Matrices of Linear Relations

A Characterization of the Essential Spectra of $$2\times 2$$ Block Matrices of Linear Relations

Demicompactness, selection of linear relation and application to multivalued matrix

Basic Notations and Results

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