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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-07-08745-X
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 $\sum _j 1-|\lambda _j|$, 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
Email: seto@kanagawa-u.ac.jp

Rongwei Yang
Affiliation: Department of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222
Email: ryang@math.albany.edu

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.