International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 31, Pages 1993-2002
Electrical Engineering Department, Catholic University of Rio de Janeiro, Rio de Janeiro 22453-900, Brazil
Received 28 June 2002
Copyright © 2003 C. S. Kubrusly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We introduce the concept of quasireducible operators. Basic properties and illustrative examples are considered in some detail in order to situate the class of quasireducible operators in its due place. In particular, it is shown that every
quasinormal operator is quasireducible. The following result links this class with the invariant subspace problem: essentially normal quasireducible operators have a
nontrivial invariant subspace, which implies that quasireducible hyponormal operators have a nontrivial invariant subspace. The paper ends with some open questions on the characterization of the class of all quasireducible operators.