Norm closed invariant subspaces in L and H

Keiji Izuchi, Daniel Suárez

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Abstract

We characterize norm closed subspaces B of L∞(∂D) such that C(∂D)B ⊂ B and maximal ones in the family of proper closed subspaces B of L∞(∂D) such that A(D)B ⊂ B, where A(D) is the disk algebra. Analogously, we characterize closed subspaces of H ∞ that are simultaneously invariant under S and S*, the forward and the backward shift operators, and maximal invariant subspaces of H∞.
Original languageEnglish
Pages (from-to)399-404
JournalGlasgow Mathematical Journal
Volume46
Issue number2
DOIs
Publication statusPublished - 1 May 2004

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