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Mixed invariant subspaces over the bidisk II
Kou Hei Izuchi
,
Kei Ji Izuchi
Abstract
For a mixed invariant subspace $N$ of $H^2$ under $T_z$ and $T^∗_w$, in the previous paper we studied the case $\mathrm{rank}[V_z ,V_w ]=1$ and either $\dim(N\ominus zN)=0$ or $1$. In this paper, we study the structure of $N$ satisfying $\mathrm{rank}[V_z ,V_w ]=1$ and $\dim(N\ominus zN)=2$. Our study is deeply concerned with the structure of nonextreme points in the closed unit ball of the space of one variable bounded analytic functions.