Generalization of some Inequalities for Matrix Exponentials to Lie Groups

Key Points

• The aim is to extend inequalities for matrix exponentials to the framework of Lie groups using Kostant's pre-order.
• Examined Kostant's pre-order on noncompact connected semisimple Lie groups.
• Generalized established inequalities from matrix theory to the context of Lie groups.
• Demonstrated the applicability of log-majorization concepts to Lie groups.
• Showed that Kostant's pre-order provides a useful framework for these generalizations.