p-Quasihyponormal operators have scalar extensions of order 6

Eungil Ko

doi:10.1016/j.jmaa.2006.07.055

p-Quasihyponormal operators have scalar extensions of order 6

Eungil Ko

Department of Mathematics

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

2 Scopus citations

Abstract

In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0 < p < 1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W² (D, H) and an operator T.

Original language	English
Pages (from-to)	80-90
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	330
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.07.055
State	Published - 1 Jun 2007

Bibliographical note

Funding Information:
✩ This work was supported by a grant (R14-2003-006-01000-0) from Korea Research Foundation. E-mail address: [email protected].

Keywords

Invariant subspaces
Scalar and subscalar operators
p-Quasihyponormal

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10.1016/j.jmaa.2006.07.055

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author = "Eungil Ko",

note = "Funding Information: ✩ This work was supported by a grant (R14-2003-006-01000-0) from Korea Research Foundation. E-mail address: [email protected].",

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N2 - In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0 < p < 1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W2 (D, H) and an operator T.

AB - In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0 < p < 1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W2 (D, H) and an operator T.

KW - Invariant subspaces

KW - Scalar and subscalar operators

KW - p-Quasihyponormal

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

p-Quasihyponormal operators have scalar extensions of order 6

Abstract

Bibliographical note

Keywords

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