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The c-numerical range of operator products on \({\mathcal {B}}(H)\)

  • Yanfang Zhang
  • Xiaochun FangEmail author
Original Paper
  • 2 Downloads

Abstract

Let \(\mathcal {H}\) be a complex Hilbert space of dimension \(\ge 2\) and \(\mathfrak {B}(\mathcal {H})\) be the algebra of all bounded linear operators on \(\mathcal {H}\). We give the form of surjective maps on \(\mathfrak {B}(\mathcal {H})\) preserving the c-numerical range of operator products when the maps preserve weak zero products. As a result, we obtain the characterization of surjective maps on \(M_n(\mathbb {C})\) preserving the c-numerical range of operator products. The proof of the results depends on some propositions of operators in \(\mathfrak {B}(\mathcal {H})\), which are of different interest.

Keywords

Preserver c-Numerical range Elliptical ranges 

Mathematics Subject Classification

47B49 47A12 

Notes

Acknowledgements

The authors wish to give their thanks to the referees for their worthy comments. This work is partially supported by National Natural Science Foundation of China (11371279, 11871375), Fundamental Research Funds for the Central Universities.

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesTongji UniversityShanghaiPeople’s Republic of China

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