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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AU - Lee, Ji Eun

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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.

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KW - Spectral radius algebra

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Remarks on Complex Symmetric Operators

Abstract

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Keywords

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