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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The isometries of $ H\sp{\infty }(K)$


Author: Michael Cambern
Journal: Proc. Amer. Math. Soc. 36 (1972), 173-178
MSC: Primary 46J15; Secondary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1972-0306921-5
MathSciNet review: 0306921
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Abstract: Let K be a finite-dimensional Hilbert space. In this article a characterization is given of the linear isometries of the Banach space $ {H^\infty }(K)$ onto itself. It is shown that T is such an isometry iff T is of the form $ (TF)(z) = \mathcal{T}F(t(z))$, for $ F \in {H^\infty }(K)$ and z belonging to the unit disc, where t is a conformal map of the disc onto itself and $ \mathcal{T}$ is an isometry of K onto K.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0306921-5
Keywords: Isometry, extreme point, maximal ideal space, Choquet boundary, Šilov boundary, representing measure
Article copyright: © Copyright 1972 American Mathematical Society