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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De Gruyter
2021
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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) |
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finite operator numerical range orthogonality class ℛ¯1 47b47 47a30 47a12 Mathematics QA1-939 |
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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 |
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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 |
| _version_ |
1718371769985794048 |