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

Abstract

In this article, we study the pseudo-Browder essential spectra of densely closed, linear operators in Banach spaces. We start by giving the definition and we investigate the characterization, the stability, and some properties of pseudo-Browder essential spectra. Finally, we apply these results to a transport equation.

A note on the essential pseudospectra and application

“…In Ammar and Jeribi [5][6][7] defined the notion of Weyl pseudospectra of densely closed defined, linear operators in the Banach space by:…”

$S$-spectra and $S$-essential pseudospectra of the diagonal block operator matrices

“…[4,8,11,15,16]. Moreover, further important characterizations concerning essential spectra and their applications to transport operators are in [1,4].…”

A characterization of the essential pseudospectra on a Banach space

“…In [1] F. Abdmouleh, A. Ammar and A. Jeribi defined the notion of pseudo-Browder essential spectra of densely closed, linear operators in the Banach space by:…”