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Conjugations in $$L^2(\mathcal {H})$$
Integral Equations and Operator Theory ( IF 0.8 ) Pub Date : 2020-10-28 , DOI: 10.1007/s00020-020-02601-9
M. Cristina Câmara , Kamila Kliś-Garlicka , Bartosz Łanucha , Marek Ptak

Conjugations commuting with $\mathbf{M}_z$ and intertwining $\mathbf{M}_z$ and $\mathbf{M}_{\bar z}$ in $L^2(\mathcal{H})$, where $\mathcal{H}$ is a Hilbert space, are characterized. We also investigate which of them leave invariant the whole Hardy space $H^2(\mathcal{H})$ or a model space $K_{\Theta}=H^2(\mathcal{H})\ominus\Theta H^2(\mathcal{H})$, where $\Theta$ is a pure operator valued inner function.

中文翻译:

$$L^2(\mathcal {H})$$ 中的共轭

与 $\mathbf{M}_z$ 交换并在 $L^2(\mathcal{H})$ 中交织 $\mathbf{M}_z$ 和 $\mathbf{M}_{\bar z}$ 的共轭,其中$\mathcal{H}$ 是一个希尔伯特空间,被表征。我们还研究了它们中的哪些在整个哈代空间 $H^2(\mathcal{H})$ 或模型空间 $K_{\Theta}=H^2(\mathcal{H})\ominus\Theta H 中保持不变^2(\mathcal{H})$,其中 $\Theta$ 是纯运算符值的内部函数。
更新日期:2020-10-28
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