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Proceedings of the American Mathematical Society

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

 

 

A note on Helson's existence theorem


Author: Jun-ichi Tanaka
Journal: Proc. Amer. Math. Soc. 69 (1978), 87-90
MSC: Primary 46J10; Secondary 30H05
DOI: https://doi.org/10.1090/S0002-9939-1978-0482594-1
MathSciNet review: 482594
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Abstract: In the almost periodic context, Helson showed that there exists a unitary function in every simply invariant subspace. We provide a short proof of this result in more general setting and give some applications.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0482594-1
Keywords: Weak-$ ^\ast$ Dirichlet algebra, invariant subspace, outer function, distant future, ergodic measure
Article copyright: © Copyright 1978 American Mathematical Society