Stability of the S-essential spectra on a Banach space

Abstract

ABSTRACT. In this paper, we give the characterization of S -essential spectra, we define the S -Riesz projection and we investigate the S -Browder resolvent. Finally, we study the S -essential spectra of sum of two bounded linear operators acting on a Banach space.

Spectral radius of S-essential spectra

“…In the particular case when the index of the operator S is equal to zero, we prove the last inequalities for the spectral radius of the S-Schechter essential spectrum. Also, we prove that the spectral radius of the S-Jeribi essential spectrum satisfies inequalities (2) when the Banach space X has no reflexive infinite dimensional subspace and the index of the operator S is equal to zero (the S-Jeribi essential spectrum, introduced in [7] as a generalisation of the Jeribi essential spectrum).…”

“…Introduction. The spectral theory of operators pencils (λS −T ) (operator-valued functions of a complex argument) play a crucial role in many branches of mathematical physics see, for example, [2,5,4,12]. The purpose of this paper is to study the spectral radius of some S-essential spectra of a bounded linear operator on a Banach space X.…”

The spectrum and the Weyr characteristics of operator pencils and linear relations

“…Qualitative properties of the solution of a classical Cauchy problem are usually described by the spectral properties of the generator. Similarly, the spectrum of the operator pencil A(λ) := λE − A describes qualitative properties of the solutions of (1).…”

“…The essential spectrum of operator pencils is also studied under the name S-essential spectrum, see [1,28] for related perturbation results and [27] for an overview.…”

A characterization of S-condition pseudospectrum of multivalued linear operators

“…In [10], A. Jeribi, N. Moalla, and S. Yengui gave a characterization of the essential spectrum of the operator pencil in order to extend many known results in the literature. After that A. Ammar, F. Abdelmouleh and A. Jeribi in [11] pursued the study of the S-essential spectra and investigated the S-Browder essential spectra of bounded linear operators on a Banach space X. To have further details of the properties of the operators pencils , we may refer to ( [3], [9]).…”