Spectral Theory and Applications of Linear Operators and Block Operator Matrices

Mathematische Nachrichten

Krichen

2015

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Key words Demicompact linear operator, essential spectrum, Fredholm and semi-Fredholm operators MSC (2010) 47A53In this paper, we present some results on Fredholm and upper semi-Fredholm operators involving demicompact operators. Our results generalize many known ones in the literature, in particular those obtained by Petryshyn in [27] and Jeribi et al. in [1], [22]. They are used to establish a fine description of the Schechter essential spectrum of closed densely defined operators, and to investigate the essential spectrum of the sum of two bounded linear operators defined on a Banach space by means of the essential spectrum of each of the two operators.

“…A similar characterization is obtained by Abdelmoumen et al. by means of the measure of noncompactness (see , ), they replaced in Eq.

{scriptM}_{n} (X)

by the set

{scriptG}_{T}^{n} (X)

defined by:

{scriptG}_{T}^{n} (X) : = \{K \in scriptL (X) such that \overset{γ}{true} ((), {([], {(λ - T - K)}^{- 1}, K)}^{n}) < \frac{1}{2} \forall λ \in ρ (T + K)\},

where

\bar{γ} (.)

denotes the measure of noncompactness of an operator (see Definition ), and they proved that for X having the D‐P property,

σ_{e_{5}} (T + K) = σ_{e_{5}} (T)

for every K in a subgroup of

{scriptG}_{T}^{n} (X)

.…”

Section: Introductionsupporting

confidence: 64%

Demicompact linear operators, essential spectrum and some perturbation results

Chaker

Mathematische Nachrichten

Krichen

2015

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“…with vacuum boundary conditions in slab geometry (see Jeribi (2002bJeribi ( , 2002cJeribi ( , 2002dJeribi ( , 2015). We define the advection operator T 0 by…”

Section: Application To a Transport Operatormentioning

confidence: 99%

A Characterization of the Pseudo-Browder Essential Spectra of Linear Operators and Application to a Transport Equation

Abdmouleh

Ammar

Journal of Computational and Theoretical Transport

2015

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“…Several papers also focused on semi-Fredholm linear relations and other classes related to them (see for example [2,6,7]). However, many authors have recently shed light on 2 × 2 operators matrices and block matrices of linear relations (see for example [1,2,5,11,15,19]). Precisely, in [19], Tretter considered X and Y as two Banach spaces, and the linear operator A as given by the block operator matrix…”

Section: Introductionmentioning

confidence: 99%

Stability of the essential spectrum of the diagonally and off-diagonally dominant block matrix linear relations

Ammar

Fakhfakh

J. Pseudo-Differ. Oper. Appl.

2016

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In the present paper, we extend in the first place the main results of Tretter in (Spectral theory block operator matrices and applications. Imperial College Press, London, 2008) to linear relations. Moreover, we define a matrix linear relation. We denote by L the block matrix linear relation, acting on the Banach space X ⊕ Y , of the formwhere A, B, C and D are four closable linear relations with dense domains. For diagonally dominant and off-diagonally dominant of block matrix linear relation L, we give a necessary and sufficient condition for L to become closed and closable. In the second place, we study the stability of the essential spectrum of this block linear relation.