Complemented invariant subspaces of $H ^p,\;0 < p < 1$, and the Hahn-Banach extension property
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- by William S. Cohn PDF
- Proc. Amer. Math. Soc. 102 (1988), 121-124 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 121-124
- MSC: Primary 46J15,; Secondary 30D55,30H05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0915728-9
- MathSciNet review: 915728