Some connections between an operator and its Helton class

Insook Kim; Yoenha Kim; Eungil Ko; Ji Eun Lee

doi:10.1016/j.jmaa.2007.09.011

Some connections between an operator and its Helton class

Insook Kim, Yoenha Kim, Eungil Ko, Ji Eun Lee

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper we show that the nilpotent perturbation of operators in the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that the nilpotent perturbation of each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has nonempty interior in the plane.

Original language	English
Pages (from-to)	1235-1240
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	340
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2007.09.011
State	Published - 15 Apr 2008

Keywords

Helton class
p-Hyponormal operators
Subscalar operators

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10.1016/j.jmaa.2007.09.011

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title = "Some connections between an operator and its Helton class",

abstract = "In this paper we show that the nilpotent perturbation of operators in the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that the nilpotent perturbation of each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has nonempty interior in the plane.",

keywords = "Helton class, p-Hyponormal operators, Subscalar operators",

author = "Insook Kim and Yoenha Kim and Eungil Ko and Lee, {Ji Eun}",

note = "Funding Information: This work is supported by a grant (R14-2003-006-01000-0) from the Korea Research Foundation. Corresponding author. E-mail addresses: ikim99@hanmail.net (I. Kim), yoenha@ewhain.net (Y. Kim), eiko@ewha.ac.kr (E. Ko), jieun7@ewhain.net (J.E. Lee).",

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T1 - Some connections between an operator and its Helton class

AU - Kim, Insook

AU - Kim, Yoenha

AU - Ko, Eungil

AU - Lee, Ji Eun

N1 - Funding Information: This work is supported by a grant (R14-2003-006-01000-0) from the Korea Research Foundation. Corresponding author. E-mail addresses: ikim99@hanmail.net (I. Kim), yoenha@ewhain.net (Y. Kim), eiko@ewha.ac.kr (E. Ko), jieun7@ewhain.net (J.E. Lee).

PY - 2008/4/15

Y1 - 2008/4/15

N2 - In this paper we show that the nilpotent perturbation of operators in the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that the nilpotent perturbation of each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has nonempty interior in the plane.

AB - In this paper we show that the nilpotent perturbation of operators in the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that the nilpotent perturbation of each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has nonempty interior in the plane.

KW - Helton class

KW - p-Hyponormal operators

KW - Subscalar operators

UR - http://www.scopus.com/inward/record.url?scp=38049007997&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2007.09.011

DO - 10.1016/j.jmaa.2007.09.011

M3 - Article

AN - SCOPUS:38049007997

SN - 0022-247X

VL - 340

SP - 1235

EP - 1240

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Some connections between an operator and its Helton class

Abstract

Keywords

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