Fredholm Operators, Essential Spectra and Application to Transport Equations

Abstract

In this paper the essential spectra of closed, densely defined linear operators is characterized on a Banach spaces under perturbations of n-strictly power compact operators. Further we apply the obtained results to investigate the essential spectra of one-dimensional transport equation with general boundary conditions and the essential spectra of singular neutron transport equations in bounded geometries. (1991): Primary 47A55, 47D03, 47N20. Mathematics Subject Classifications

Essential Spectra, Matrix Operator and Applications

“…So, let μ ∈ ρ(A 1 ). Then On the other hand, the fact that Cσ e5 (A) (resp., Cσ e5 (M μ )) is connected and ρ(A) = ∅ (resp., ρ(M μ ) = ∅) together with Lemma 3.1 in [13] make us deduce that σ e5 (A) = σ e6 (A) (resp., σ e5 (M μ ) = σ e6 (M μ )). Now, using the relation (3.8) and arguing as above, we derive easily the result for σ e6 (·).…”

Stability of the S-essential spectra on a Banach space

“…The subsets σ e1,I (·) and σ e2,I (·) are the Gustafson and Weidmann essential spectra [2], σ e3,I (·) is the Kato essential spectrum [15], σ e4,I (·) is the Wolf essential spectrum [2-5, 9, 25, 26], σ e5,I (·) is the Schechter essential spectrum [2,[6][7][8][9]20,21], σ e6,I (·) denotes the Browder essential spectrum [2,9,10,13,18], σ e7,I (·) was introduced by V. Rakocević in [19] and designates the essential approximate point spectrum and σ e8,I (·) is the essential defect spectrum and was introduced by V. Schmoeger [23].…”

On a characterization of the essential spectra of some matrix operators and application to two-group transport operators

“…the Gustafson and Weidmann essential spectra [12] and σ ess (.) the Schechter essential spectrum [12,[14][15][16]26,27]. σ eap (.)…”