Abstract
For a subset $E$ of the bidisc $D^2, M=\{f\in H^2(D^2)~:~f=0$ on $E\}$ and $N$ is the orthogonal complement of $M$ in $H^2(D^2)$ where $H^2(D^2)$ is the two variable Hardy space on $D^2$. We describe the finite rank commutants of the restricted shifts $S_z$ and $S_w$ on $N$ when $E$ satisfies some natural condition. Moreover we give a sufficient condition for that the Pick interpolation is possible.
Citation
Takahiko Nakazi. "Commutators of two compressed shifts and the Hardy space on the bidisc." Ann. Funct. Anal. 5 (2) 47 - 52, 2014. https://doi.org/10.15352/afa/1396833501
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