Abstract
Let $\mathfrak M$ be an invariant subspace of $L^2(\mathbb{T}^2)$. Considering the largest z-invariant (resp. $w$-invariant) subspace $\mathfrak {F}_z$ (resp. $\mathfrak {F}_w)$ in the wandering subspace $M \ominus zw{\mathfrak{M}}$ of $\mathfrak{M}$ with respect to the shift operator $zw$. If $\mathfrak{F}_w \ne \{0\}$ and $\mathfrak{F}_z \ne \{0\}$, then we consider the certain form of invariant subspaces $\mathfrak{M}$ of $L^2(T^2)$. Furthermore, we study certain classes of invariant subspaces of $L^2(T^2)$.
Citation
Atsushi HASEGAWA. Guoxing JI. Tomoyoshi OHWADA. Kichi-Suke SAITO. "Certain invariant subspace structure of $L^2(\Bbb T^2)$ II." Hokkaido Math. J. 37 (3) 493 - 505, August 2008. https://doi.org/10.14492/hokmj/1253539532
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