Some Results on Fredholm Operators, Essential Spectra, and Application

Abstract

In this paper, after a characterization of a class of bounded Fredholm operators on Banach spaces, we investigate the essential spectra of closed, densely defined linear operators on L spaces. The obtained results are used to describe the p essential spectra of one-dimensional transport equations with general boundary conditions. ᮊ

Exponential trend to equilibrium for the inelastic Boltzmann equation driven by a particle bath

“…However, it can be shown that in L 1 -spaces it is actually stable under weakly compact perturbations, see [14,Theorem 3.2 & Remark 3.3]. Due to this property we have…”

Fredholm Operators, Essential Spectra and Application to Transport Equations

“…More precisely, let X be a Banach space and let A 2 CðXÞ. If J is n-strictly power compact operator on X (see Definition In general, in applications [11,26,27,36,44], these results are not applicable directly, so practical criterions which guarantee the invariance of the Wolf and Schechter essential spectra for perturbed linear operators are provided (Theorems 3.2 and 3.3). Also, we point out that the definition of ' e5 (.)…”

“…Thus, Theorem 3.4 provides an improvement of the definition of the Schechter essential spectrum on Banach spaces. Also, it may be regarded as an extension of Theorem 3.1 in[27] to general Banach spaces in terms of operators in M n ðXÞ.…”

“…The purpose of this work is to pursue the analysis started in [12,18,23] and [27], and to extend it to general Banach spaces under perturbations belonging to M n ðX Þ which is not a two-sided ideal of LðXÞ. More precisely, let X be a Banach space and let A 2 CðXÞ.…”

“…This work is inspired by [12Y14, 18,27] where essential spectra of operators in CðL p Þ are discussed on L p spaces. The analysis uses the concept of strictly singular operators (see Definition 2.3) which possess some nice properties on these spaces (cf.…”