Hokkaido Mathematical Journal

Rank-one commutators on invariant subspaces of the Hardy space on the bidisk III

Kou Hei IZUCHI

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Abstract

We study a special type of invariant subspaces ${\mathcal M}$ on the bidisk which are studied in the previous papers. We determine the rank of cross commutators on $H^2\ominus {\mathcal M}$, and study when ${\mathcal M}$ is generated by ${\mathcal M}\ominus (z{\mathcal M}+w{\mathcal M})$ as an invariant subspace of $H^2$.

Article information

Source
Hokkaido Math. J., Volume 38, Number 4 (2009), 663-681.

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1258554239

Digital Object Identifier
doi:10.14492/hokmj/1258554239

Mathematical Reviews number (MathSciNet)
MR2561955

Zentralblatt MATH identifier
1191.47006

Subjects
Primary: 47A15: Invariant subspaces [See also 47A46]
Secondary: 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]

Keywords
invariant subspaces backward shift invariant subspaces rank-one commutators

Citation

IZUCHI, Kou Hei. Rank-one commutators on invariant subspaces of the Hardy space on the bidisk III. Hokkaido Math. J. 38 (2009), no. 4, 663--681. doi:10.14492/hokmj/1258554239. https://projecteuclid.org/euclid.hokmj/1258554239


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