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Complex symmetric operators and additive preservers problem

  • Zouheir AmaraEmail author
  • Mourad Oudghiri
  • Khalid Souilah
Original Paper

Abstract

Given a conjugation C on a separable complex Hilbert space H, a bounded linear operator T on H is said to be C-symmetric if \(CTC=T^*\), and is said to be C-skew symmetric if \(CTC=-\,T^*\). In this paper, we provide a complete description of all additive maps, on the algebra of all bounded linear operators acting on H, that preserve C-symmetric operators for every conjugation C. We focus also on the linear maps preserving C-skew symmetric operators.

Keywords

Linear preservers problem Complex symmetric operators Diagonal operators 

Mathematics Subject Classification

47B49 47B99 47C15 

Notes

Acknowledgements

The authors would like to thank the referee for carefully reading our manuscript and making many valuable suggestions which served to improve this paper, especially for drawing our attention to the linear preservers problem of skew-symmetric operators.

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  • Zouheir Amara
    • 1
    Email author
  • Mourad Oudghiri
    • 1
  • Khalid Souilah
    • 1
  1. 1.Department of Mathematics, Labo LAGA, Faculty of SciencesMohamed Premier UniversityOujdaMorocco

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