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A norm inequality on noncommutative symmetric spaces related to a question of Bourin
Published 14 Apr 2024 in math.FA | (2404.09250v1)
Abstract: In this note, we study a question introduced by Bourin \cite{2009Matrix} and partially solve the question of Bourin. In fact, for t\in[0,\frac{1}{4}]\cup[\frac{3}{4},1], we show that |||x{t}y{1-t}+y{t}x{1-t}|||\leq|||x+y|||, where x,y\in\mathbb{M}_{n}(\mathbb{C})+ and ||\cdot|| is the unitarily invariant norm. Moreover, we prove that the above inequality holds on noncommutative fully symmetric spaces.
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