Subscalarity of (p,k)-quasihyponormal operators

Sungeun Jung; Eungil Ko; Mee Jung Lee

doi:10.1016/j.jmaa.2011.02.063

Subscalarity of (p,k)-quasihyponormal operators

Sungeun Jung, Eungil Ko, Mee Jung Lee

Department of Mathematics

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

5 Scopus citations

Abstract

In this paper, we show that every (p,k)-quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of (p,k)-quasihyponormal operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace. Finally, we prove that the sum of a p-hyponormal operator and an algebraic operator which are commuting is subscalar.

Original language	English
Pages (from-to)	76-86
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	380
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.02.063
State	Published - 1 Aug 2011

Keywords

(p,k)-Quasihyponormal operator
Algebraic operator
Invariant subspace
P-Hyponormal operator
Subscalar operator

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10.1016/j.jmaa.2011.02.063

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title = "Subscalarity of (p,k)-quasihyponormal operators",

abstract = "In this paper, we show that every (p,k)-quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of (p,k)-quasihyponormal operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace. Finally, we prove that the sum of a p-hyponormal operator and an algebraic operator which are commuting is subscalar.",

keywords = "(p,k)-Quasihyponormal operator, Algebraic operator, Invariant subspace, P-Hyponormal operator, Subscalar operator",

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note = "Funding Information: ✩ This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). * Corresponding author. E-mail addresses: ssung105@ewhain.net (S. Jung), eiko@ewha.ac.kr (E. Ko), meejung@ewhain.net (M. Lee).",

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AU - Lee, Mee Jung

N1 - Funding Information: ✩ This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). * Corresponding author. E-mail addresses: ssung105@ewhain.net (S. Jung), eiko@ewha.ac.kr (E. Ko), meejung@ewhain.net (M. Lee).

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N2 - In this paper, we show that every (p,k)-quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of (p,k)-quasihyponormal operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace. Finally, we prove that the sum of a p-hyponormal operator and an algebraic operator which are commuting is subscalar.

AB - In this paper, we show that every (p,k)-quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of (p,k)-quasihyponormal operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace. Finally, we prove that the sum of a p-hyponormal operator and an algebraic operator which are commuting is subscalar.

KW - (p,k)-Quasihyponormal operator

KW - Algebraic operator

KW - Invariant subspace

KW - P-Hyponormal operator

KW - Subscalar operator

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DO - 10.1016/j.jmaa.2011.02.063

M3 - Article

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VL - 380

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EP - 86

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Subscalarity of (p,k)-quasihyponormal operators

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Keywords

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