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
$\|x^{t}y^{1-t}+y^{t}x^{1-t}\|_{E(\mathcal{M})}\leq2^{2t-\frac{3}{2}}\|x+y\|_{E(\mathcal{M})}.$
Jinchen LIU
,
Kan HE
,
Xingpeng ZHAO*
. A NORM INEQUALITY ON NONCOMMUTATIVE SYMMETRIC SPACES RELATED TO A QUESTION OF BOURIN[J]. Acta mathematica scientia, Series B, 2026
, 46(1)
: 62
-68
.
DOI: 10.1007/s10473-026-0104-7
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