Annals of Functional Analysis

Commutators of two compressed shifts and the Hardy space on the bidisc

Takahiko Nakazi

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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.

Article information

Source
Ann. Funct. Anal., Volume 5, Number 2 (2014), 47-52.

Dates
First available in Project Euclid: 7 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1396833501

Digital Object Identifier
doi:10.15352/afa/1396833501

Mathematical Reviews number (MathSciNet)
MR3192008

Zentralblatt MATH identifier
1306.47033

Subjects
Primary: 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
Secondary: 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]

Keywords
restricted shift commutant finite rank bidisc

Citation

Nakazi, Takahiko. Commutators of two compressed shifts and the Hardy space on the bidisc. Ann. Funct. Anal. 5 (2014), no. 2, 47--52. doi:10.15352/afa/1396833501. https://projecteuclid.org/euclid.afa/1396833501


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References

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