Spectral Theory For Strongly Continuous Cosine

Let (C(t))t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ2 is al...

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Auteur principal:	Boua Hamid
Format:	article
Langue:	EN
Publié:	De Gruyter 2021
Sujets:	cosine semi-fredholm drazin invertible semi-browder left essentially drazin invertible right essentially drazin invertible 47d09 47a11 Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/5f90dd5c0a22451ca71aa175ff851058
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spelling	oai:doaj.org-article:5f90dd5c0a22451ca71aa175ff8510582021-12-05T14:10:45ZSpectral Theory For Strongly Continuous Cosine2299-328210.1515/conop-2020-0110https://doaj.org/article/5f90dd5c0a22451ca71aa175ff8510582021-03-01T00:00:00Zhttps://doi.org/10.1515/conop-2020-0110https://doaj.org/toc/2299-3282Let (C(t))t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ2 is also. We show by counterexample that the converse is false in general.Boua HamidDe Gruyterarticlecosinesemi-fredholmdrazin invertiblesemi-browderleft essentially drazin invertibleright essentially drazin invertible47d0947a11MathematicsQA1-939ENConcrete Operators, Vol 8, Iss 1, Pp 40-47 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	cosine semi-fredholm drazin invertible semi-browder left essentially drazin invertible right essentially drazin invertible 47d09 47a11 Mathematics QA1-939
spellingShingle	cosine semi-fredholm drazin invertible semi-browder left essentially drazin invertible right essentially drazin invertible 47d09 47a11 Mathematics QA1-939 Boua Hamid Spectral Theory For Strongly Continuous Cosine
description	Let (C(t))t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ2 is also. We show by counterexample that the converse is false in general.
format	article
author	Boua Hamid
author_facet	Boua Hamid
author_sort	Boua Hamid
title	Spectral Theory For Strongly Continuous Cosine
title_short	Spectral Theory For Strongly Continuous Cosine
title_full	Spectral Theory For Strongly Continuous Cosine
title_fullStr	Spectral Theory For Strongly Continuous Cosine
title_full_unstemmed	Spectral Theory For Strongly Continuous Cosine
title_sort	spectral theory for strongly continuous cosine
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/5f90dd5c0a22451ca71aa175ff851058
work_keys_str_mv	AT bouahamid spectraltheoryforstronglycontinuouscosine
_version_	1718371763114475520

Spectral Theory For Strongly Continuous Cosine

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