Kth roots of p-hyponormal operators are subscalar operators of order 4k

Eungil Ko

doi:10.1007/s00020-007-1519-8

Kth roots of p-hyponormal operators are subscalar operators of order 4k

Eungil Ko

Department of Mathematics

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

14 Scopus citations

Abstract

In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if T ^k is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if T ^k is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.

Original language	English
Pages (from-to)	173-187
Number of pages	15
Journal	Integral Equations and Operator Theory
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s00020-007-1519-8
State	Published - Oct 2007

Bibliographical note

Funding Information:
The work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD, Basic Research Promotion Fund) (KRF-2006-312-C00461).

Keywords

Invariant subspace
P-hyponormality
Subscalarity
The property (β)

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10.1007/s00020-007-1519-8

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abstract = "In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if T k is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if T k is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.",

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N2 - In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if T k is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if T k is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.

AB - In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if T k is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if T k is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.

KW - Invariant subspace

KW - P-hyponormality

KW - Subscalarity

KW - The property (β)

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ER -

Kth roots of p-hyponormal operators are subscalar operators of order 4k

Abstract

Bibliographical note

Keywords

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