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

6 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

Bibliographical 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: [email protected] (S. Jung), [email protected] (E. Ko), [email protected] (M. Lee).

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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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.

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KW - Invariant subspace

KW - P-Hyponormal operator

KW - Subscalar operator

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JO - Journal of Mathematical Analysis and Applications

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Subscalarity of (p,k)-quasihyponormal operators

Abstract

Bibliographical note

Keywords

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