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The isometries of $ H\sp 1\sb \mathcal{H}$


Authors: Michael Cambern and Krzysztof Jarosz
Journal: Proc. Amer. Math. Soc. 107 (1989), 205-214
MSC: Primary 46E40; Secondary 43A17, 46J15, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1989-0979225-8
MathSciNet review: 979225
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Abstract: Let $ \mathcal{H}$ be a finite-dimensional complex Hilbert space. In this article we characterize the linear isometries of the Banach space $ H_\mathcal{H}^1$ onto itself. We show that $ T$ is such an isometry iff $ T$ is of the form $ TF(z) = UF(\psi (z))\psi '(z)$, for $ F \in H_\mathcal{H}^1$ and $ z$ in the unit disc, where $ \psi $ is a conformal map of the disc onto itself, and $ U$ is a unitary operator on $ \mathcal{H}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0979225-8
Article copyright: © Copyright 1989 American Mathematical Society

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