On subscalarity of some 2 × 2 class A operator matrices

Eungil Ko; Sungeun Jung; Yoenha Kim

doi:10.1016/j.laa.2012.08.037

On subscalarity of some 2 × 2 class A operator matrices

Eungil Ko, Sungeun Jung, Yoenha Kim

Department of Mathematics

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

4 Scopus citations

Abstract

In this paper we provide some conditions for 2×2 operator matrices whose diagonal entries are class A operators to be subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. In addition, we show that the tensor product of a 2×2 upper triangular class A operator matrix and a class A operator has a scalar extension. Finally, we find some subscalar 2×2 operator matrices satisfying the operator equations ABA=A² and BAB=B².

Original language	English
Pages (from-to)	1322-1338
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	3
DOIs	https://doi.org/10.1016/j.laa.2012.08.037
State	Published - 1 Feb 2013

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 (2012-0006691). The second author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [NRF-2011-355-1-C00005]. E-mail addresses: [email protected] (S. Jung), [email protected] (Y. Kim), [email protected] (E. Ko).

Keywords

Class A operator
Invariant subspace
Subscalar

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10.1016/j.laa.2012.08.037

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abstract = "In this paper we provide some conditions for 2×2 operator matrices whose diagonal entries are class A operators to be subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. In addition, we show that the tensor product of a 2×2 upper triangular class A operator matrix and a class A operator has a scalar extension. Finally, we find some subscalar 2×2 operator matrices satisfying the operator equations ABA=A2 and BAB=B2.",

keywords = "Class A operator, Invariant subspace, Subscalar",

author = "Eungil Ko and Sungeun Jung and Yoenha Kim",

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 (2012-0006691). The second author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [NRF-2011-355-1-C00005]. E-mail addresses: [email protected] (S. Jung), [email protected] (Y. Kim), [email protected] (E. Ko).",

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AU - Kim, Yoenha

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N2 - In this paper we provide some conditions for 2×2 operator matrices whose diagonal entries are class A operators to be subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. In addition, we show that the tensor product of a 2×2 upper triangular class A operator matrix and a class A operator has a scalar extension. Finally, we find some subscalar 2×2 operator matrices satisfying the operator equations ABA=A2 and BAB=B2.

AB - In this paper we provide some conditions for 2×2 operator matrices whose diagonal entries are class A operators to be subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. In addition, we show that the tensor product of a 2×2 upper triangular class A operator matrix and a class A operator has a scalar extension. Finally, we find some subscalar 2×2 operator matrices satisfying the operator equations ABA=A2 and BAB=B2.

KW - Class A operator

KW - Invariant subspace

KW - Subscalar

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EP - 1338

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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ER -

On subscalarity of some 2 × 2 class A operator matrices

Abstract

Bibliographical note

Keywords

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