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Certain invariant subspace structure of $L^{2}( \mathbb{T}^{2})$

Authors: Guoxing Ji, Tomoyoshi Ohwada and Kichi-Suke Saito
Journal: Proc. Amer. Math. Soc. 126 (1998), 2361-2368
MSC (1991): Primary 47A15; Secondary 46J15
MathSciNet review: 1451811
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Abstract: In this note, we study certain structure of an invariant subspace $ \mathfrak{M}$ of $L^{2}(\mathbb{T}^{2})$. Considering the largest $z$-invariant (resp. $w$-invariant) subspace in the wandering subspace $\mathfrak{M} \ominus zw \mathfrak{M}$ of $\mathfrak{M}$ with respect to the shift operator $zw$, we give an alternative characterization of Beurling-type invariant subspaces. Furthermore, we consider a certain class of invariant subspaces.

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Additional Information

Guoxing Ji
Affiliation: Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, 950-21, Japan

Tomoyoshi Ohwada

Kichi-Suke Saito
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-21, Japan

Received by editor(s): April 9, 1996
Received by editor(s) in revised form: January 21, 1997
Additional Notes: This work was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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