Inner sequence based invariant subspaces in $H^{2}(D^2)$
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- by Michio Seto and Rongwei Yang PDF
- Proc. Amer. Math. Soc. 135 (2007), 2519-2526 Request permission
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.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2302572