A characterization of submodules via the Beurling-Lax-Halmos theorem
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Abstract:
Shift invariant subspaces in the vector-valued Hardy space $H^2(E)$ play important roles in Nagy-Foias operator model theory. A theorem by Beurling, Lax and Halmos characterizes such invariant subspaces by operator-valued inner functions $\Theta (z)$. When $E=H^2(\mathbb {D})$, $H^2(E)$ is the Hardy space over the bidisk $H^2(\mathbb {D}^2)$. This paper shows that for some well-known examples of invariant subspaces in $H^{2}({\mathbb {D}}^2)$, the function $\Theta (z)$ turns out to be strikingly simple.References
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Additional Information
- Yueshi Qin
- Affiliation: Department of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222
- Email: yqin@albany.edu
- Rongwei Yang
- Affiliation: Department of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222
- Email: ryang@albany.edu
- Received by editor(s): September 24, 2012
- Received by editor(s) in revised form: October 19, 2012
- Published electronically: June 18, 2014
- Communicated by: Pamela B. Gorkin
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3505-3510
- MSC (2010): Primary 47A45; Secondary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-2014-12081-8
- MathSciNet review: 3238425