Abstract
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 language | English |
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Pages (from-to) | 83-91 |
Number of pages | 9 |
Journal | Integral Equations and Operator Theory |
Volume | 55 |
Issue number | 1 |
DOIs | |
State | Published - May 2006 |
Keywords
- Sub-Jordan operator
- Sub-n-normal operator
- Subnormal operator