Abstract
This paper studies a question of Bourin on noncommutative spaces. Some inequalities due to Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin II. Int J Math. 2021;32:2150043] and Hayajneh et al. [Norm inequalities for positive semidefinite matrices and a question of Bourin III. Positivity. 2022;26:23] are extended to the case of operators in noncommutative spaces associated with a semifinite von Neumann algebra. We give a partial answer to a question of Bourin on noncommutative spaces. Some related submajorization inequalities are also given.
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