TY - JOUR
AU - Belabbaci, C.
PY - 2020/10/06
Y2 - 2021/11/28
TI - Spectral radius of S-essential spectra
JF - Matematychni Studii
JA - Mat. Stud.
VL - 54
IS - 1
SE - Articles
DO - 10.30970/ms.54.1.91-97
UR - http://matstud.org.ua/ojs/index.php/matstud/article/view/22
SP - 91-97
AB - In this paper, we study the spectral radius of some S-essential spectra of a bounded linear operator defined on a Banach space. More precisely, via the concept of measure of noncompactness,we show that for any two bounded linear operators $T$ and $S$ with $S$ non zero and non compact operator the spectral radius of the S-Gustafson, S-Weidmann, S-Kato and S-Wolf essential spectra are given by the following inequalities\begin{equation}\dfrac{\beta(T)}{\alpha(S)}\leq r_{e, S}(T)\leq \dfrac{\alpha(T)}{\beta(S)},\end{equation}where $\alpha(.)$ stands for the Kuratowski measure of noncompactness and $\beta(.)$ is defined in [11].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).
ER -