SPECTRAL RADIUS OF S-ESSENTIAL SPECTRA
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Date
2021
Authors
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Journal ISSN
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Publisher
Université de M'sila
Abstract
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
(T)
(S)
re;S(T)
(T)
(S)
; (1)
where (:) stands for the Kuratowski measure of noncompactness and (:) 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).