New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal

A new class of operators, larger than ∗\ast -finite operators, named generalized ∗\ast -finite operators and noted by Gℱ∗(ℋ){{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }}) is introduced, where: Gℱ∗(ℋ)={(A,B)∈ℬ(ℋ)×ℬ(ℋ):∥TA−BT∗−λI∥≥∣λ∣,∀λ∈C,∀T∈ℬ(ℋ)}.{{\mathcal{G {\mathcal F} }}}...

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Autores principales:	Messaoudene Hadia, Mesbah Nadia
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	∗-finite operator numerical range generalized jordan ∗-derivation finite operator paranormal operator 47b47 47a12 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/20f9be0886aa4fbcbf6da4add912de44
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spelling	oai:doaj.org-article:20f9be0886aa4fbcbf6da4add912de442021-12-05T14:10:45ZNew class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal2391-466110.1515/dema-2021-0032https://doaj.org/article/20f9be0886aa4fbcbf6da4add912de442021-08-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0032https://doaj.org/toc/2391-4661A new class of operators, larger than ∗\ast -finite operators, named generalized ∗\ast -finite operators and noted by Gℱ∗(ℋ){{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }}) is introduced, where: Gℱ∗(ℋ)={(A,B)∈ℬ(ℋ)×ℬ(ℋ):∥TA−BT∗−λI∥≥∣λ∣,∀λ∈C,∀T∈ℬ(ℋ)}.{{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }})=\{(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}):\parallel TA-B{T}^{\ast }-\lambda I\parallel \ge \| \lambda \| ,\hspace{0.33em}\forall \lambda \in {\mathbb{C}},\hspace{0.33em}\forall T\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\}. Basic properties are given. Some examples are also presented.Messaoudene HadiaMesbah NadiaDe Gruyterarticle∗-finite operatornumerical rangegeneralized jordan ∗-derivationfinite operatorparanormal operator47b4747a12MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 311-317 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	∗-finite operator numerical range generalized jordan ∗-derivation finite operator paranormal operator 47b47 47a12 Mathematics QA1-939
spellingShingle	∗-finite operator numerical range generalized jordan ∗-derivation finite operator paranormal operator 47b47 47a12 Mathematics QA1-939 Messaoudene Hadia Mesbah Nadia New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal
description	A new class of operators, larger than ∗\ast -finite operators, named generalized ∗\ast -finite operators and noted by Gℱ∗(ℋ){{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }}) is introduced, where: Gℱ∗(ℋ)={(A,B)∈ℬ(ℋ)×ℬ(ℋ):∥TA−BT∗−λI∥≥∣λ∣,∀λ∈C,∀T∈ℬ(ℋ)}.{{\mathcal{G {\mathcal F} }}}^{\ast }\left({\mathcal{ {\mathcal H} }})=\{(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}):\parallel TA-B{T}^{\ast }-\lambda I\parallel \ge \| \lambda \| ,\hspace{0.33em}\forall \lambda \in {\mathbb{C}},\hspace{0.33em}\forall T\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\}. Basic properties are given. Some examples are also presented.
format	article
author	Messaoudene Hadia Mesbah Nadia
author_facet	Messaoudene Hadia Mesbah Nadia
author_sort	Messaoudene Hadia
title	New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal
title_short	New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal
title_full	New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal
title_fullStr	New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal
title_full_unstemmed	New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal
title_sort	new class of operators where the distance between the identity operator and the generalized jordan ∗-derivation range is maximal
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/20f9be0886aa4fbcbf6da4add912de44
work_keys_str_mv	AT messaoudenehadia newclassofoperatorswherethedistancebetweentheidentityoperatorandthegeneralizedjordanderivationrangeismaximal AT mesbahnadia newclassofoperatorswherethedistancebetweentheidentityoperatorandthegeneralizedjordanderivationrangeismaximal
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New class of operators where the distance between the identity operator and the generalized Jordan ∗-derivation range is maximal

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