Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (1): 62-68.doi: 10.1007/s10473-026-0104-7

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A NORM INEQUALITY ON NONCOMMUTATIVE SYMMETRIC SPACES RELATED TO A QUESTION OF BOURIN

Jinchen LIU, Kan HE, Xingpeng ZHAO*   

  1. Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
  • Received:2024-11-25 Revised:2025-04-14 Online:2026-01-25 Published:2026-05-22
  • Contact: * Xingpeng Zhao, E-mail:zhaoxingpeng1@sina.com
  • About author:Jinchen LIU, E-mail:2276063895@qq.com; Kan HE, hekanquantum@163.com
  • Supported by:
    The third author was supported by the Fundamental Research Program of Shanxi Province (202103021223038).

Abstract: In this note, we study a question introduced by Bourin [1] and extend the conclusion from [2] to the case of operators on noncommutative fully symmetric spaces. The conclusion is as follows. Let $0\leq x,y\in E(\mathcal{M})$, If $t\in[0,\frac{1}{4}]\cup[\frac{3}{4},1]$, then
$\|x^{t}y^{1-t}+y^{t}x^{1-t}\|_{E(\mathcal{M})}\leq2^{2t-\frac{3}{2}}\|x+y\|_{E(\mathcal{M})}.$

Key words: $\tau$-measurable operators, fully symmetric spaces, von Neumann algebra

CLC Number: 

  • 47A30
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