Norm closed invariant subspaces in L∞ and H ∞

Keiji Izuchi; Daniel Suárez

doi:10.1017/S0017089504001880

Norm closed invariant subspaces in L^∞ and H ^∞

Keiji Izuchi, Daniel Suárez

Research output: Contribution to journal › Article › Research › peer-review

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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 language	English
Pages (from-to)	399-404
Journal	Glasgow Mathematical Journal
Volume	46
Issue number	2
DOIs	https://doi.org/10.1017/S0017089504001880
Publication status	Published - 1 May 2004

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title = "Norm closed invariant subspaces in L∞ and H ∞",

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∞.",

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N2 - 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∞.

AB - 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∞.

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DO - 10.1017/S0017089504001880

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JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

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Norm closed invariant subspaces in L∞ and H ∞

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Norm closed invariant subspaces in L^∞ and H ^∞