A norm inequality on noncommutative symmetric spaces related to a question of Bourin

2024/04/14 by Jinchen Liu, Liu, Jinchen, Kan He +3
Mathematics · #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2404.09250

openalex publication_date 2024/04/14 · openalex created_date 2024/04/17 · openalex updated_date 2026/07/28

Abstract

In this note, we study a question introduced by Bourin \cite2009Matrix and partially solve the question of Bourin. In fact, for t∈[0,(1)/(4)]∪[(3)/(4),1], we show that |||x^ty^1-t+y^tx^1-t|||≤|||x+y|||, where x,y∈\mathbbM_n(ℂ)⁺ and ‖|⋅‖| is the unitarily invariant norm. Moreover, we prove that the above inequality holds on noncommutative fully symmetric spaces.

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