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.
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.