Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces

Let ℋ{\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ(ℋ){\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ{\mathcal{ {\mathcal H} }}. In this paper, we present some new pairs of generalized finite operators. More pre...

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Autores principales:	Mesbah Nadia, Messaoudene Hadia, Alharbi Asma
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	finite operator numerical range orthogonality class ℛ¯1 47b47 47a30 47a12 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/c7595c086d1a4502998eb95fe51b1362
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spelling	oai:doaj.org-article:c7595c086d1a4502998eb95fe51b13622021-12-05T14:10:45ZSome results on generalized finite operators and range kernel orthogonality in Hilbert spaces2391-466110.1515/dema-2021-0037https://doaj.org/article/c7595c086d1a4502998eb95fe51b13622021-10-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0037https://doaj.org/toc/2391-4661Let ℋ{\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ(ℋ){\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ{\mathcal{ {\mathcal H} }}. In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators (A,B)∈ℬ(ℋ)×ℬ(ℋ)\left(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) satisfying: ∥AX−XB−I∥≥1,for allX∈ℬ(ℋ).\parallel AX-XB-I\parallel \ge 1,\hspace{1.0em}\hspace{0.1em}\text{for all}\hspace{0.1em}\hspace{0.33em}X\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.Mesbah NadiaMessaoudene HadiaAlharbi AsmaDe Gruyterarticlefinite operatornumerical rangeorthogonalityclass ℛ¯147b4747a3047a12MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 318-325 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	finite operator numerical range orthogonality class ℛ¯1 47b47 47a30 47a12 Mathematics QA1-939
spellingShingle	finite operator numerical range orthogonality class ℛ¯1 47b47 47a30 47a12 Mathematics QA1-939 Mesbah Nadia Messaoudene Hadia Alharbi Asma Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
description	Let ℋ{\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ(ℋ){\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ{\mathcal{ {\mathcal H} }}. In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators (A,B)∈ℬ(ℋ)×ℬ(ℋ)\left(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) satisfying: ∥AX−XB−I∥≥1,for allX∈ℬ(ℋ).\parallel AX-XB-I\parallel \ge 1,\hspace{1.0em}\hspace{0.1em}\text{for all}\hspace{0.1em}\hspace{0.33em}X\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.
format	article
author	Mesbah Nadia Messaoudene Hadia Alharbi Asma
author_facet	Mesbah Nadia Messaoudene Hadia Alharbi Asma
author_sort	Mesbah Nadia
title	Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
title_short	Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
title_full	Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
title_fullStr	Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
title_full_unstemmed	Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
title_sort	some results on generalized finite operators and range kernel orthogonality in hilbert spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/c7595c086d1a4502998eb95fe51b1362
work_keys_str_mv	AT mesbahnadia someresultsongeneralizedfiniteoperatorsandrangekernelorthogonalityinhilbertspaces AT messaoudenehadia someresultsongeneralizedfiniteoperatorsandrangekernelorthogonalityinhilbertspaces AT alharbiasma someresultsongeneralizedfiniteoperatorsandrangekernelorthogonalityinhilbertspaces
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Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces

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