ROSENTHAL INEQUALITIES IN NONCOMMUTATIVE SYMMETRIC SPACES

Abstract. We give a direct proof of the `upper ' Khintchine inequality for a noncommutative symmetric (quasi-)Banach function space with nontrivial up-per Boyd index. This settles an open question of C. Le Merdy and the fourth named author [24]. We apply this result to derive a version of Rosenthal's theorem for sums of independent random variables in a noncommutative sym-metric space. As a result we obtain a new proof of Rosenthal's theorem for (Haagerup) Lp-spaces. 1