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

Departament de Matemàtiques

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Resum

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∞.

Idioma original	Anglès
Pàgines (de-a)	399-404
Revista	Glasgow Mathematical Journal
Volum	46
Número	2
DOIs	https://doi.org/10.1017/S0017089504001880
Estat de la publicació	Publicada - 1 de maig 2004

Accés al document

10.1017/S0017089504001880

Com citar-ho

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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∞.",

author = "Keiji Izuchi and Daniel Su{\'a}rez",

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AU - Suárez, Daniel

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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∞.

U2 - 10.1017/S0017089504001880

DO - 10.1017/S0017089504001880

M3 - Article

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VL - 46

SP - 399

EP - 404

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

IS - 2

ER -

Norm closed invariant subspaces in L∞ and H ∞

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