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Inner sequence based invariant subspaces in $ H^{2}(D^2)$

Authors: Michio Seto and Rongwei Yang
Journal: Proc. Amer. Math. Soc. 135 (2007), 2519-2526
MSC (2000): Primary 47A13; Secondary 46E20
Published electronically: March 2, 2007
MathSciNet review: 2302572
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Abstract: A closed subspace $ H^{2}(D^2)$ is said to be invariant if it is invariant under the Toeplitz operators $ T_z$ and $ T_w$. Invariant subspaces of $ H^{2}(D^2)$ are well-known to be very complicated. So discovering some good examples of invariant subspaces will be beneficial to the general study. This paper studies a type of invariant subspace constructed through a sequence of inner functions. It will be shown that this type of invariant subspace has direct connections with the Jordan operator. Related calculations also give rise to a simple upper bound for $ \sum_j 1-\vert\lambda_j\vert$, where $ \{\lambda_j\}$ are zeros of a Blaschke product.

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Additional Information

Michio Seto
Affiliation: Department of Mathematics, Kanagawa University, Yokohama, Japan

Rongwei Yang
Affiliation: Department of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222

Keywords: Core operator, Hardy space over the bidisk, Jordan operator, Blaschke product
Received by editor(s): November 4, 2005
Received by editor(s) in revised form: April 6, 2006
Published electronically: March 2, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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