Some remarks on noncommutative Khintchine inequalities

Normalized free semi-circular random variables satisfy an upper Khintchine inequality in $L_\infty$. We show that this implies the corresponding upper Khintchine inequality in any noncommutative Banach function space. As applications, we obtain a very simple proof of a well-known interpolation result for row and column operator spaces and, moreover, answer an open question on noncommutative moment inequalities concerning a paper by Bekjan and Chen.

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