Some notes on complex symmetric operators
In this paper we show that every conjugation $C$ on the Hardy-Hilbert space $H^{2}$ is of type $C=T^{*}\mathcal{J} T$, where $T$ is an unitary operator and $\mathcal{J} f\left(z\right)=\overline{f\left(\overline{z}\right)}$ with $f\in H^{2}$. Moreover, we prove some relations of complex symmetry bet...
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EJAAM
2021-12-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2021/10.2478-ejaam-2021-0006.pdf |
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| author | Marcos S. Ferreira |
| author_facet | Marcos S. Ferreira |
| author_sort | Marcos S. Ferreira |
| collection | DOAJ |
| description | In this paper we show that every conjugation $C$ on the Hardy-Hilbert space $H^{2}$ is of type $C=T^{*}\mathcal{J} T$, where $T$ is an unitary operator and $\mathcal{J} f\left(z\right)=\overline{f\left(\overline{z}\right)}$ with $f\in H^{2}$. Moreover, we prove some relations of complex symmetry between the operators $T$ and $\left|T\right|$, where $T =U\left|T\right|$ is the polar decomposition of bounded operator $T\in\mathcal{L}\left(\mathcal{H}\right)$ on the separable Hilbert space $\mathcal{H}$. |
| format | Article |
| id | doaj-art-755e7d9e7219414ea05eaa006380e35a |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2021-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-755e7d9e7219414ea05eaa006380e35a2025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902021-12-01202110.2478/ejaam-2021-0006Some notes on complex symmetric operatorsMarcos S. Ferreira0Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual de Santa Cruz, Ilhéus, Bahia, BrasilIn this paper we show that every conjugation $C$ on the Hardy-Hilbert space $H^{2}$ is of type $C=T^{*}\mathcal{J} T$, where $T$ is an unitary operator and $\mathcal{J} f\left(z\right)=\overline{f\left(\overline{z}\right)}$ with $f\in H^{2}$. Moreover, we prove some relations of complex symmetry between the operators $T$ and $\left|T\right|$, where $T =U\left|T\right|$ is the polar decomposition of bounded operator $T\in\mathcal{L}\left(\mathcal{H}\right)$ on the separable Hilbert space $\mathcal{H}$.https://ejaam.org/articles/2021/10.2478-ejaam-2021-0006.pdfhardy spacetoeplitz operatorcomplex symmetric operatoraluthge transform |
| spellingShingle | Marcos S. Ferreira Some notes on complex symmetric operators E-Journal of Analysis and Applied Mathematics hardy space toeplitz operator complex symmetric operator aluthge transform |
| title | Some notes on complex symmetric operators |
| title_full | Some notes on complex symmetric operators |
| title_fullStr | Some notes on complex symmetric operators |
| title_full_unstemmed | Some notes on complex symmetric operators |
| title_short | Some notes on complex symmetric operators |
| title_sort | some notes on complex symmetric operators |
| topic | hardy space toeplitz operator complex symmetric operator aluthge transform |
| url | https://ejaam.org/articles/2021/10.2478-ejaam-2021-0006.pdf |
| work_keys_str_mv | AT marcossferreira somenotesoncomplexsymmetricoperators |