scholarly journals Fredholm, Semi-Fredholm Perturbations, and Essential Spectra

2001 ◽  
Vol 259 (1) ◽  
pp. 277-301 ◽  
Author(s):  
Khalid Latrach ◽  
Abdelkader Dehici
Keyword(s):  
Essential Spectra ◽  
Fredholm Perturbations

scholarly journals Relatively compact-like perturbations, essential spectra and application

2004 ◽  
Vol 77 (1) ◽  
pp. 73-90 ◽  
Author(s):  
Khalid Latrach ◽  
J. Martin Paoli
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Neutron Transport ◽  
Linear Operators ◽  
Essential Spectra ◽  
Graph Norm ◽  
Bounded Linear ◽  
Neutron Transport Equations ◽  
Densely Defined ◽  
Fredholm Perturbations

AbstractThe purpose of this paper is to provide a detailed treatment of the behaviour of essential spectra of closed densely defined linear operators subjected to additive perturbations not necessarily belonging to any ideal of the algebra of bounded linear operators. IfAdenotes a closed densely defined linear operator on a Banach spaceX, our approach consists principally in considering the class ofA-closable operators which, regarded as operators in ℒ(XA,X) (whereXAdenotes the domain ofAequipped with the graph norm), are contained in the set ofA-Fredholm perturbations (see Definition 1.2). Our results are used to describe the essential spectra of singular neutron transport equations in bounded geometries.

scholarly journals Fredholm perturbations and seminorms related to upper semi-Fredholm perturbations

Filomat ◽  
2013 ◽  
Vol 27 (6) ◽  
pp. 1147-1155 ◽  
Author(s):  
Boulbeba Abdelmoumen ◽  
Hamadi Baklouti
Keyword(s):  
Fredholm Perturbations

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

scholarly journals Dirichlet and Neumann eigenvalues for half-plane magnetic Hamiltonians

2014 ◽  
Vol 26 (02) ◽  
pp. 1450003 ◽  
Author(s):  
Vincent Bruneau ◽  
Pablo Miranda ◽  
Georgi Raikov
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behavior ◽  
Half Plane ◽  
Compact Support ◽  
Constant Magnetic Field ◽  
Scalar Potential ◽  
Neumann Boundary ◽  
Essential Spectra ◽  
Neumann Eigenvalues ◽  
Effective Hamiltonians

Let H0,D (respectively, H0,N) be the Schrödinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let Hℓ := H0,ℓ - V, ℓ = D, N, where the scalar potential V is non-negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of HD and HN below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behavior of the discrete spectrum of Hℓ near inf σ ess (Hℓ) = inf σ(H0,ℓ), ℓ = D, N. Applying these Hamiltonians, we show that σ disc (HD) is infinite even if V has a compact support, while σ disc (HN) could be finite or infinite depending on the decay rate of V.

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