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Mediterranean Journal of Mathematics

, Volume 13, Issue 2, pp 719–728 | Cite as

Remarks on Complex Symmetric Operators

  • Sungeun Jung
  • Eungil Ko
  • Ji Eun Lee
Article
  • 109 Downloads

Abstract

An operator \({T\in{\mathcal{L}}({\mathcal{H}})}\) is said to be complex symmetric if there exists a conjugation C on \({{\mathcal H}}\) such that \({T= CT^{\ast}C}\). 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 \({{\mathcal B}_{A}}\) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between \({P_{\tilde{A}}}\) and \({P_{\widetilde{A^{\ast}}}}\) (defined below) when A is complex symmetric.

Keywords

Complex symmetric operator Invariant subspace Spectral radius algebra 

Mathematics Subject Classification

Primary 47A15 47A65 Secondary 47B49 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsEwha Womans UniversitySeoulKorea
  2. 2.Institute of Mathematical SciencesEwha Womans UniversitySeoulKorea
  3. 3.Department of Mathematics, Applied StatisticsSejong UniversitySeoulKorea

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