A characterization of essential pseudospectra of the multivalued operator matrix

Ammar, Aymen; Jeribi, Aref; Saadaoui, Bilel

doi:10.1007/s13324-017-0170-z

Cited by 12 publications

(2 citation statements)

References 18 publications

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“…A number of authors have studied properties of M C in the recent past, including the spectrum, essential spectrum, Browder spectrum, Weyl spectrum, etc. (see [11][12][13][14][15][16][17][18][19][20]). In this paper, we consider the boundedness below for M C , where A,B,C are all linear relations.…”

Section: Introductionmentioning

confidence: 99%

The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices

Ran Huo,

Yanyan Du,

Junjie Huang

2024

JMS

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In this note, the boundedness below of linear relation matrix), H,K are separable Hilbert spaces. By suitable space decompositions, a necessary and sufficient condition for diagonal relations A,B is given so that M C is bounded below for some C ∈ BLR(K, H). Besides, the characterization of σ ap (M C ) and σ su (M C ) are obtained, and the relationship between σ ap (M 0 ) and σ ap (M C ) is further presented.

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Section: Introductionmentioning

confidence: 99%

The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices

Ran Huo,

Yanyan Du,

Junjie Huang

2024

JMS

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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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Essential spectra of upper triangular relation matrices

Huang

2022

Monatsh Math

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A characterization of essential pseudospectra of the multivalued operator matrix

Cited by 12 publications

References 18 publications

The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices

The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices

Demicompactness, selection of linear relation and application to multivalued matrix

Essential spectra of upper triangular relation matrices

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