On scalar extensions and spectral decompositions of complex symmetric operators

Sungeun Jung; Eungil Ko; Ji Eun Lee

doi:10.1016/j.jmaa.2011.05.056

On scalar extensions and spectral decompositions of complex symmetric operators

Sungeun Jung, Eungil Ko, Ji Eun Lee

Department of Mathematics

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

22 Scopus citations

Abstract

In this paper we prove that a complex symmetric operator with property (Δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints.

Original language	English
Pages (from-to)	252-260
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	384
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.05.056
State	Published - 15 Dec 2011

Bibliographical note

Funding Information:
✩ This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MEST) (2010-0001983). The third author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [KRF-2010-355-C00005]. * Corresponding author. E-mail addresses: [email protected] (S. Jung), [email protected] (E. Ko), [email protected] (J.E. Lee).

Keywords

Complex symmetric operator
Decomposable
Property (Δ)
Spectral decompositions
Subscalar

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10.1016/j.jmaa.2011.05.056

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title = "On scalar extensions and spectral decompositions of complex symmetric operators",

abstract = "In this paper we prove that a complex symmetric operator with property (Δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints.",

keywords = "Complex symmetric operator, Decomposable, Property (Δ), Spectral decompositions, Subscalar",

author = "Sungeun Jung and Eungil Ko and Lee, {Ji Eun}",

note = "Funding Information: ✩ This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MEST) (2010-0001983). The third author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [KRF-2010-355-C00005]. * Corresponding author. E-mail addresses: [email protected] (S. Jung), [email protected] (E. Ko), [email protected] (J.E. Lee).",

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doi = "10.1016/j.jmaa.2011.05.056",

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T1 - On scalar extensions and spectral decompositions of complex symmetric operators

AU - Jung, Sungeun

AU - Ko, Eungil

AU - Lee, Ji Eun

N1 - Funding Information: ✩ This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MEST) (2010-0001983). The third author was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Education, Science and Technology) [KRF-2010-355-C00005]. * Corresponding author. E-mail addresses: [email protected] (S. Jung), [email protected] (E. Ko), [email protected] (J.E. Lee).

PY - 2011/12/15

Y1 - 2011/12/15

N2 - In this paper we prove that a complex symmetric operator with property (Δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints.

AB - In this paper we prove that a complex symmetric operator with property (Δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints.

KW - Complex symmetric operator

KW - Decomposable

KW - Property (Δ)

KW - Spectral decompositions

KW - Subscalar

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SP - 252

EP - 260

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On scalar extensions and spectral decompositions of complex symmetric operators

Abstract

Bibliographical note

Keywords

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