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

• Published in: Glasgow mathematical journal Vol. 46; no. 2; pp. 399 - 404
• Main Authors: IZUCHI, KEIJI, SUÁREZ, DANIEL
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.05.2004
• Subjects: Primary 47A15; Secondary 46J15; Primary 47A15; Secondary 46J15
• ISSN: 0017-0895; 1469-509X
• DOI: 10.1017/S0017089504001880

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 $H^\infty$.