A norm inequality on noncommutative symmetric spaces related to a question of Bourin
Abstract
In this note, we study a question introduced by Bourin 2009Matrix and partially solve the question of Bourin. In fact, for t∈[0,14][34,1], we show that |||xty1-t+ytx1-t|||≤|||x+y|||, where x,y∈Mn(C)+ and \||·\|| is the unitarily invariant norm. Moreover, we prove that the above inequality holds on noncommutative fully symmetric spaces.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.