The isometries of $H^ 1_ \mathcal {H}$
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- by Michael Cambern and Krzysztof Jarosz PDF
- Proc. Amer. Math. Soc. 107 (1989), 205-214 Request permission
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 $\mathcal {H}$.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- 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