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Quasireducible operators

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  • C. S. Kubrusly

Abstract

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.

Suggested Citation

  • C. S. Kubrusly, 2003. "Quasireducible operators," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:198750
    DOI: 10.1155/S0161171203206165
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