NORM CLOSED INVARIANT SUBSPACES IN $L^{\infty}$ AND $H^\infty
We characterize norm closed subspaces $B$ of $\linf (\partial D)$ such that $C(\partial D) B \subset B$ and maximal ones in the family of proper closed subspaces $B$ of $L^\infty(\partial D)$ such that $A(D) B \subset B$, where $A(D)$ is the disk algebra. Analogously, we characterize closed subspace...
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Published in | Glasgow mathematical journal Vol. 46; no. 2; pp. 399 - 404 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
01.05.2004
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Subjects | |
Online Access | Get full text |
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Summary: | We characterize norm closed subspaces $B$ of $\linf (\partial D)$ such that $C(\partial D) B \subset B$ and maximal ones in the family of proper closed subspaces $B$ of $L^\infty(\partial D)$ such that $A(D) B \subset B$, where $A(D)$ is the disk algebra. Analogously, we characterize closed subspaces of $H^\infty$ that are simultaneously invariant under $S$ and $S^\ast$, the forward and the backward shift operators, and maximal invariant subspaces of $H^\infty$. |
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Bibliography: | ark:/67375/6GQ-HTWSG9B4-S istex:9F796D751EF4470D0533BECA287FBF4BB6066832 PII:S0017089504001880 |
ISSN: | 0017-0895 1469-509X |
DOI: | 10.1017/S0017089504001880 |