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NORM CLOSED INVARIANT SUBSPACES IN $L^{\infty}$ AND $H^\infty$

Published online by Cambridge University Press:  19 May 2004

KEIJI IZUCHI  and
DANIEL SUÁREZ
KEIJI IZUCHI
Affiliation:
Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-21, Japan e-mail: izuchi@math.sc.niigata-u.ac.jp
DANIEL SUÁREZ
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain e-mail: dsuarez@mat.uab.es
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Abstract

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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 $H^\infty$.

Keywords

Primary 47A15Secondary 46J15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 2 , May 2004 , pp. 399 - 404
Copyright
2004 Glasgow Mathematical Journal Trust