Certain invariant subspace structure of 𝐿²(𝕋²)

Ji, Guoxing; Ohwada, Tomoyoshi; Saito, Kichi-Suke

doi:10.1090/S0002-9939-98-04341-X

Certain invariant subspace structure of $L^2(\mathbb T^2)$
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by Guoxing Ji, Tomoyoshi Ohwada and Kichi-Suke Saito

Proc. Amer. Math. Soc. 126 (1998), 2361-2368

DOI: https://doi.org/10.1090/S0002-9939-98-04341-X

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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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