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Chunlan Jiang and Rongwei Yang
Jordan blocks and strong irreducibility view print
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| Published: |
September 9, 2011
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| Keywords: |
Jordan block, strong irreducibility |
| Subject: |
Primary 47B38, Secondary 47A65 |
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Abstract
An operator is said to be strongly irreducible if its commutant has no nontrivial
idempotent. This paper first shows that if an operator is not strongly irreducible then the
set of idempotents in its commutant is either finite or uncountable. The second part of the paper focuses on
the Jordan block which is a well-known class of irreducible operators, and determines when a Jordan block
is strongly irreducible. This work is an interplay of operator theory and complex function theory.
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| Acknowledgements
The first author is supported by 973 Project of China and the National Science Foundation of China.
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| Author information
Chunlan Jiang:
Department of Mathematics, Hebei Normarl University, Shijiazhuang, China
cljiang@mail.hebtu.edu.cn
Rongwei Yang:
Department of Mathematics and Statistics, SUNY at Albany, Albany, NY 12047, U.S.A.
ryang@math.albany.edu
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