Reducing subspaces for a class of multiplication operators on the Dirichlet space

Author:
Liankuo Zhao

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3091-3097

MSC (2000):
Primary 47A15, 46E22; Secondary 47S99.

Published electronically:
March 11, 2009

MathSciNet review:
2506467

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we discuss reducing subspaces of multiplication operators on the Dirichlet space defined by a Blaschke product with two zeros , in the unit disk and show that when , has two proper ones; otherwise it has none. This is different from the cases of the Hardy space and the Bergman space.

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Additional Information

**Liankuo Zhao**

Affiliation:
School of Mathematics and Computer Science, Shanxi Normal University, Linfen, 041004, People’s Republic of China

Email:
lkzhao@sxnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-09-09859-1

Keywords:
Reducing subspace,
multiplication operator,
Dirichlet space

Received by editor(s):
June 25, 2008

Received by editor(s) in revised form:
December 17, 2008

Published electronically:
March 11, 2009

Communicated by:
Nigel J. Kalton

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.