Remarks on Complex Symmetric Operators

Sungeun Jung; Eungil Ko; Ji Eun Lee

doi:10.1007/s00009-015-0520-8

Remarks on Complex Symmetric Operators

Sungeun Jung, Eungil Ko, Ji Eun Lee

Department of Mathematics

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

1 Scopus citations

Abstract

An operator (Formula presented.) is said to be complex symmetric if there exists a conjugation C on (Formula presented.) such that (Formula presented.). In this paper, we study the spectral radius algebras for complex symmetric operators. In particular, we prove that if A is a complex symmetric operator, then the spectral radius algebra (Formula presented.) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between (Formula presented.) and (Formula presented.) (defined below) when A is complex symmetric.

Original language	English
Pages (from-to)	719-728
Number of pages	10
Journal	Mediterranean Journal of Mathematics
Volume	13
Issue number	2
DOIs	https://doi.org/10.1007/s00009-015-0520-8
State	Published - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Basel.

Keywords

Complex symmetric operator
Invariant subspace
Spectral radius algebra

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10.1007/s00009-015-0520-8

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abstract = "An operator (Formula presented.) is said to be complex symmetric if there exists a conjugation C on (Formula presented.) such that (Formula presented.). In this paper, we study the spectral radius algebras for complex symmetric operators. In particular, we prove that if A is a complex symmetric operator, then the spectral radius algebra (Formula presented.) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between (Formula presented.) and (Formula presented.) (defined below) when A is complex symmetric.",

keywords = "Complex symmetric operator, Invariant subspace, Spectral radius algebra",

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

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AU - Jung, Sungeun

AU - Ko, Eungil

AU - Lee, Ji Eun

PY - 2016/4/1

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N2 - An operator (Formula presented.) is said to be complex symmetric if there exists a conjugation C on (Formula presented.) such that (Formula presented.). In this paper, we study the spectral radius algebras for complex symmetric operators. In particular, we prove that if A is a complex symmetric operator, then the spectral radius algebra (Formula presented.) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between (Formula presented.) and (Formula presented.) (defined below) when A is complex symmetric.

AB - An operator (Formula presented.) is said to be complex symmetric if there exists a conjugation C on (Formula presented.) such that (Formula presented.). In this paper, we study the spectral radius algebras for complex symmetric operators. In particular, we prove that if A is a complex symmetric operator, then the spectral radius algebra (Formula presented.) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between (Formula presented.) and (Formula presented.) (defined below) when A is complex symmetric.

KW - Complex symmetric operator

KW - Invariant subspace

KW - Spectral radius algebra

UR - https://www.scopus.com/pages/publications/84921887328

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SP - 719

EP - 728

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 2

ER -

Remarks on Complex Symmetric Operators

Abstract

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Keywords

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