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Rosenthal inequalities in noncommutative symmetric spaces. (English) Zbl 1267.46076

Summary: We give a direct proof of the ‘upper’ Khintchine inequality for a noncommutative symmetric (quasi-)Banach function space with nontrivial upper Boyd index. This settles an open question of C. Le Merdy and F. Sukochev [J. Funct. Anal. 255, No. 12, 3329–3355 (2008; Zbl 1247.46050)]. We apply this result to derive a version of Rosenthal’s theorem for sums of independent random variables in a noncommutative symmetric space. As a result, we obtain a new proof of Rosenthal’s theorem for (Haagerup) \(L^p\)-spaces.

MSC:

46L52 Noncommutative function spaces

Citations:

Zbl 1247.46050
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