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Proceedings of the American Mathematical Society

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

 

 

Complemented invariant subspaces of $ H ^p,\;0 < p < 1$, and the Hahn-Banach extension property


Author: William S. Cohn
Journal: Proc. Amer. Math. Soc. 102 (1988), 121-124
MSC: Primary 46J15,; Secondary 30D55,30H05
MathSciNet review: 915728
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Abstract: Let $ 0{\text{ < }}p{\text{ < }}1$ and let $ {H^p}$ denote the usual Hardy class of functions analytic on the disc. In this note we show that an invariant subspace of $ {H^p}$ is complemented in $ {H^p}$ if and only if it has the form $ B{H^p}$ where $ B$ is a Blaschke product whose zero sequence is a Carleson sequence. We also prove that this occurs if and only if the invariant subspace has the Hahn-Banach extension property.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0915728-9
Keywords: Complemented invariant subspace, Blaschke product, Carleson sequence, Hahn-Banach extension property
Article copyright: © Copyright 1988 American Mathematical Society