Sub-n-normal Operators

Il Bong Jung, Eungil Ko, Carl Pearcy

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper we introduce the class of sub-n-norrnal operators. By definition, such an operator is the restriction to an invariant subspace of an n-normal operator, and thus the sub-n-normal operators form a larger class than the subnormal operators. We obtain some modest structure theorems and contrast sub-n-normal operators with sub-Jordan operators. Finally we show that a sub-n-normal operator with rich spectrum has a nontrivial invariant subspace.

Original languageEnglish
Pages (from-to)83-91
Number of pages9
JournalIntegral Equations and Operator Theory
Issue number1
StatePublished - May 2006

Bibliographical note

Funding Information:
Problem 6.4. Does the converse of Theorem 2.4 hold? (It is known to hold for subnormal operators.) Acknowledgement. The first and second authors were supported by a grant from KOSEF, R14-2003-006-01000-0. The third author acknowledges the support of the National Science Foundation.


  • Sub-Jordan operator
  • Sub-n-normal operator
  • Subnormal operator


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