A note on an inequality involving Jordan product in Euclidean Jordan algebras

摘要

In a most recent paper, Yang et al. (Appl Math Comput 230:616-628, 2014) proved an important inequality on a simple Euclidean Jordan algebra by using a case-by-case analysis. In this paper, we improve this inequality in any Euclidean Jordan algebras and the proof is not based on a case-by-case analysis.