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Additivity of maps preserving Jordan triple products on prime \(C^*\)-algebras

  • Ali TaghaviEmail author
  • Ensiyeh Tavakoli
Original Paper

Abstract

Let \( \mathcal {A} \) and \(\mathcal {B}\) be two unital \(C^*\)-algebras such that \( \mathcal {A} \) contains a non-trivial projection \(P_1\). In this paper, we investigate the additivity of maps \( \varPhi \) from \(\mathcal {A}\) onto \(\mathcal {B}\) that are bijective maps, that satisfy
$$\begin{aligned} \varPhi \left( \frac{AB^*C+CB^*A}{2} \right) =\frac{\varPhi (A)\varPhi (B)^*\varPhi (C)+\varPhi (C)\varPhi (B)^*\varPhi (A)}{2} \end{aligned}$$
for every \( A, B, C\in \mathcal {A}\). Moreover if \( \mathcal {B} \) is a prime \(C^*\)-algebra and \( \varPhi (I)\) is a positive element, then \( \varPhi \) is a \(*\)-isomorphism.

Keywords

Preservers Jordan triple Prime \(C^*\)-algebra 

Mathematics Subject Classification

46J10 47B48 

Notes

Acknowledgements

The authors would like to thank anonymous reviewer for a thorough and detailed report with many helpful comments and suggestions.

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran

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