Inner sequence based invariant subspaces in

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 | References | Similar Articles | Additional Information

Abstract: A closed subspace is said to be invariant if it is invariant under the Toeplitz operators and . Invariant subspaces of 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 , where 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

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-08745-X

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.