Notes on centralizing traces and Lie triple isomorphisms on triangular algebras

Abstract

The aim of the paper is to give a condition on which every centralizing trace of a bilinear map on triangular algebras is commuting. As an application, we give a short proof of a result due to Xiao et al. As another application, we give a description of Lie triple isomorphisms of certain triangular algebras, which improves a result due to Xiao et al.

Keywords:

• centralizing trace
• commuting trace
• Lie triple isomorphism
• triangular algebra

AMS Subject Classifications:

• 15A78
• 47L35
• 16W25

Acknowledgements

The author would like to thank the referee for his/her valuable comments.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The work is supported in part by the Natural Science Foundation of Shanghai Municipal Science and Technology Commission [grant number 14ZR1431200].