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

2021 ◽  
Author(s):  
Aymen Ammar ◽  
Aicha Ezzadam ◽  
Aref Jeribi
Keyword(s):  
Essential Spectra ◽  
Block Matrices ◽  
Linear Relations

A characterization of some subsets of S-essential spectra of a multivalued linear operator

2014 ◽  
Vol 135 (2) ◽  
pp. 171-186 ◽  
Author(s):  
Teresa Álvarez ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Linear Operator ◽  
Essential Spectra ◽  
Multivalued Linear Operator

Left-right fredholm and left-right browder linear relations

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 255-271 ◽  
Author(s):  
T. Álvarez ◽  
Fatma Fakhfakh ◽  
Maher Mnif
Keyword(s):  
Banach Space ◽  
Finite Rank ◽  
Linear Relation ◽  
Finite Rank Operator ◽  
Linear Relations ◽  
Rank Operator ◽  
Type Decomposition ◽  
Converse Results

In this paper we introduce the notions of left (resp. right) Fredholm and left (resp. right) Browder linear relations. We construct a Kato-type decomposition of such linear relations. The results are then applied to give another decomposition of a left (resp. right) Browder linear relation T in a Banach space as an operator-like sum T = A + B, where A is an injective left (resp. a surjective right) Fredholm linear relation and B is a bounded finite rank operator with certain properties of commutativity. The converse results remain valid with certain conditions of commutativity. As a consequence, we infer the characterization of left (resp. right) Browder spectrum under finite rank operator.

Some properties of upper triangular $$3\times 3$$ 3 × 3 -block matrices of linear relations

2015 ◽  
Vol 8 (3) ◽  
pp. 189-204 ◽  
Author(s):  
Aymen Ammar ◽  
Mohammed Zerai Dhahri ◽  
Aref Jeribi
Keyword(s):  
Block Matrices ◽  
Linear Relations

Stability of the S-essential spectra on a Banach space

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Faiçal Abdmouleh ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Essential Spectra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Projection

AbstractIn this paper, we give the characterization of S-essential spectra, we define the S-Riesz projection and we investigate the S-Browder resolvent. Finally, we study the S-essential spectra of sum of two bounded linear operators acting on a Banach space.

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