@article{Belabbaci_2020, title={Spectral radius of S-essential spectra}, volume={54}, url={http://matstud.org.ua/ojs/index.php/matstud/article/view/22}, DOI={10.30970/ms.54.1.91-97}, abstractNote={<p>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<br>\begin{equation}<br>\dfrac{\beta(T)}{\alpha(S)}\leq r_{e, S}(T)\leq \dfrac{\alpha(T)}{\beta(S)},<br>\end{equation}<br>where $\alpha(.)$ stands for the Kuratowski measure of noncompactness and $\beta(.)$ is defined in [11].<br>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]<br>as a generalisation of the Jeribi essential spectrum).</p>}, number={1}, journal={Matematychni Studii}, author={Belabbaci, C.}, year={2020}, month={Oct.}, pages={91-97} }