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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
EJAAM
2021-12-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
| Subjects: | |
| Online Access: | https://ejaam.org/articles/2021/10.2478-ejaam-2021-0006.pdf |
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| Summary: | 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 $\mathcal{H}$. |
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| ISSN: | 2544-9990 |