A characterization of submodules via the beurling-lax-halmos theorem

Yueshi Qin; Rongwei Yang

doi:10.1090/S0002-9939-2014-12081-8

A characterization of submodules via the beurling-lax-halmos theorem

Yueshi Qin
, Rongwei Yang

Mathematics and Statistics

University at Albany

SUNY Albany

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

5 Scopus citations

Abstract

Shift invariant subspaces in the vector-valued Hardy space H²(E) play important roles in Nagy-Foias operator model theory. A theorem by Beurling, Lax and Halmos characterizes such invariant subspaces by operatorvalued inner functions Θ(z). When E = H²(D), H²(E) is the Hardy space over the bidisk H²(D²). This paper shows that for some well-known examples of invariant subspaces in H²(D²), the function Θ (z) turns out to be strikingly simple.

Original language	English
Pages (from-to)	3505-3510
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	142
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-2014-12081-8
State	Published - Oct 1 2014

Keywords

Hardy space over the bidisk
Operator inner function
Spectrum
Submodule

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10.1090/S0002-9939-2014-12081-8

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abstract = "Shift invariant subspaces in the vector-valued Hardy space H2(E) play important roles in Nagy-Foias operator model theory. A theorem by Beurling, Lax and Halmos characterizes such invariant subspaces by operatorvalued inner functions Θ(z). When E = H2(D), H2(E) is the Hardy space over the bidisk H2(D2). This paper shows that for some well-known examples of invariant subspaces in H2(D2), the function Θ (z) turns out to be strikingly simple.",

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AB - Shift invariant subspaces in the vector-valued Hardy space H2(E) play important roles in Nagy-Foias operator model theory. A theorem by Beurling, Lax and Halmos characterizes such invariant subspaces by operatorvalued inner functions Θ(z). When E = H2(D), H2(E) is the Hardy space over the bidisk H2(D2). This paper shows that for some well-known examples of invariant subspaces in H2(D2), the function Θ (z) turns out to be strikingly simple.

KW - Hardy space over the bidisk

KW - Operator inner function

KW - Spectrum

KW - Submodule

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JF - Proceedings of the American Mathematical Society

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A characterization of submodules via the beurling-lax-halmos theorem

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Keywords

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