Quasireducible operators

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 resul...

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Bibliographic Details
Main Author: C. S. Kubrusly
Format: Article
Language:English
Published: Wiley 2003-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171203206165
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Summary: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.
ISSN:0161-1712
1687-0425