Open AccessSpectral radius of S-essential spectra
Author(s) -
C. Belabbaci
Publication year - 2020
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.54.1.91-97
Subject(s) - mathematics , spectral radius , essential spectrum , spectrum (functional analysis) , banach space , bounded function , bounded operator , zero (linguistics) , radius , measure (data warehouse) , operator (biology) , compact operator , spectral line , mathematical analysis , subspace topology , pure mathematics , eigenvalues and eigenvectors , physics , quantum mechanics , chemistry , philosophy , computer security , repressor , database , linguistics , computer science , biochemistry , transcription factor , programming language , extension (predicate logic) , gene
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).