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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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:
  • Rongwei Yang
  • Affiliation: Department of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222
  • Email:
  • 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:
  • MathSciNet review: 2302572