Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>

Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>

In this paper, we analyze local spectral properties of operators <inline-formula><math display="inline"><semantics><mrow><mi>R</mi><mo>,</mo></mrow></semantics></math></inline-formula><i>S</i> and <inlin...

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Main Author: Salvatore Triolo
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Axioms
Subjects:
local spectral subspaces
Dunford’s property (<i>C</i>) and property (<i>β</i>)
Drazin invertible operators
Online Access:https://www.mdpi.com/2075-1680/9/4/120
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author Salvatore Triolo
author_facet Salvatore Triolo
author_sort Salvatore Triolo
collection DOAJ
description In this paper, we analyze local spectral properties of operators <inline-formula><math display="inline"><semantics><mrow><mi>R</mi><mo>,</mo></mrow></semantics></math></inline-formula><i>S</i> and <inline-formula><math display="inline"><semantics><mrow><mi>R</mi><mi>S</mi></mrow></semantics></math></inline-formula> which satisfy the operator equations <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mi>n</mi></msup><mi>S</mi><msup><mi>R</mi><mi>n</mi></msup><mo>=</mo><msup><mi>R</mi><mi>j</mi></msup></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msup><mi>S</mi><mi>n</mi></msup><mi>R</mi><msup><mi>S</mi><mi>n</mi></msup><mo>=</mo><msup><mi>S</mi><mi>j</mi></msup></mrow></semantics></math></inline-formula> for same integers <inline-formula><math display="inline"><semantics><mrow><mi>j</mi><mo>≥</mo><mi>n</mi><mo>≥</mo><mn>0</mn><mo>.</mo></mrow></semantics></math></inline-formula> We also continue to study the relationship between the local spectral properties of an operator <i>R</i> and the local spectral properties of <inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mo>.</mo></mrow></semantics></math></inline-formula> Thus, we investigate the transmission of some local spectral properties from <i>R</i> to <i>S</i> and we illustrate our results with an example. The theory is exemplified in some cases.
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spelling doaj.art-303fbde6b9d64a119537ea0a914528d72023-11-20T17:39:53ZengMDPI AGAxioms2075-16802020-10-019412010.3390/axioms9040120Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>Salvatore Triolo0Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, ItalyIn this paper, we analyze local spectral properties of operators <inline-formula><math display="inline"><semantics><mrow><mi>R</mi><mo>,</mo></mrow></semantics></math></inline-formula><i>S</i> and <inline-formula><math display="inline"><semantics><mrow><mi>R</mi><mi>S</mi></mrow></semantics></math></inline-formula> which satisfy the operator equations <inline-formula><math display="inline"><semantics><mrow><msup><mi>R</mi><mi>n</mi></msup><mi>S</mi><msup><mi>R</mi><mi>n</mi></msup><mo>=</mo><msup><mi>R</mi><mi>j</mi></msup></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msup><mi>S</mi><mi>n</mi></msup><mi>R</mi><msup><mi>S</mi><mi>n</mi></msup><mo>=</mo><msup><mi>S</mi><mi>j</mi></msup></mrow></semantics></math></inline-formula> for same integers <inline-formula><math display="inline"><semantics><mrow><mi>j</mi><mo>≥</mo><mi>n</mi><mo>≥</mo><mn>0</mn><mo>.</mo></mrow></semantics></math></inline-formula> We also continue to study the relationship between the local spectral properties of an operator <i>R</i> and the local spectral properties of <inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mo>.</mo></mrow></semantics></math></inline-formula> Thus, we investigate the transmission of some local spectral properties from <i>R</i> to <i>S</i> and we illustrate our results with an example. The theory is exemplified in some cases.https://www.mdpi.com/2075-1680/9/4/120local spectral subspacesDunford’s property (<i>C</i>) and property (<i>β</i>)Drazin invertible operators
spellingShingle Salvatore Triolo
Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>
Axioms
local spectral subspaces
Dunford’s property (<i>C</i>) and property (<i>β</i>)
Drazin invertible operators
title Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>
title_full Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>
title_fullStr Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>
title_full_unstemmed Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>
title_short Local Spectral Theory for <i>R</i> and <i>S</i> Satisfying <i>R<sup>n</sup>SR<sup>n</sup></i> = <i>R<sup>j</sup></i>
title_sort local spectral theory for i r i and i s i satisfying i r sup n sup sr sup n sup i i r sup j sup i
topic local spectral subspaces
Dunford’s property (<i>C</i>) and property (<i>β</i>)
Drazin invertible operators
url https://www.mdpi.com/2075-1680/9/4/120
work_keys_str_mv AT salvatoretriolo localspectraltheoryfoririandisisatisfyingirsupnsupsrsupnsupiirsupjsupi

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