Sub-n-normal Operators

Il Bong Jung; Eungil Ko; Carl Pearcy

doi:10.1007/s00020-005-1374-4

Sub-n-normal Operators

Il Bong Jung, Eungil Ko, Carl Pearcy

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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
Pages (from-to)	83-91
Number of pages	9
Journal	Integral Equations and Operator Theory
Volume	55
Issue number	1
DOIs	https://doi.org/10.1007/s00020-005-1374-4
State	Published - 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.

Keywords

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

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10.1007/s00020-005-1374-4

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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.",

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AU - Pearcy, Carl

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N2 - 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.

AB - 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.

KW - Sub-Jordan operator

KW - Sub-n-normal operator

KW - Subnormal operator

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SP - 83

EP - 91

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

ER -

Sub-n-normal Operators

Abstract

Bibliographical note

Keywords

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