New York Journal of Mathematics
Volume 17 (2011) 619-626


Chunlan Jiang and Rongwei Yang

Jordan blocks and strong irreducibility

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Published: September 9, 2011
Keywords: Jordan block, strong irreducibility
Subject: Primary 47B38, Secondary 47A65

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.


The first author is supported by 973 Project of China and the National Science Foundation of China.

Author information

Chunlan Jiang:
Department of Mathematics, Hebei Normarl University, Shijiazhuang, China

Rongwei Yang:
Department of Mathematics and Statistics, SUNY at Albany, Albany, NY 12047, U.S.A.