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Proceedings of the American Mathematical Society

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



Isometries of $ H\sp{p}$ spaces of the torus

Authors: Nand Lal and Samuel Merrill
Journal: Proc. Amer. Math. Soc. 31 (1972), 465-471
MSC: Primary 46E15
MathSciNet review: 0296676
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Abstract: Denote by $ {H^p}(1 \leqq p \leqq \infty )$ the Banach spaces of complex-valued functions in $ {L^p}$ of the torus whose Fourier coefficients vanish off a half plane determined by a lexicographic ordering. The surjective isometries of the spaces $ {H^p}(p \ne 2)$ are characterized in terms of unimodular functions on the circle and conformal maps of the disc. For $ 1 < p < \infty (p \ne 2)$ the proof depends upon a characterization of certain invariant subspaces previously given by the authors.

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Keywords: $ {H^p}$ spaces, isometries, torus, invariant subspace, conformal map, logmodular algebra, double Fourier coefficients
Article copyright: © Copyright 1972 American Mathematical Society