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Certain invariant subspace structure of
Authors:Guoxing Ji  Tomoyoshi Ohwada  Kichi-Suke Saito
Institution:Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, 950-21, Japan ; Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, 950-21, Japan ; Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-21, Japan
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.

Keywords:
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