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Rosenthal inequalities in noncommutative symmetric spaces |
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| Authors: | Sjoerd Dirksen Ben de Pagter |
| Institution: | a Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands b School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia |
| Abstract: | 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 the fourth named author (Le Merdy and Sukochev, 2008 24]). 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) Lp-spaces. |
| Keywords: | Khintchine inequalities Burkholder-Gundy inequalities Rosenthal inequalities Noncommutative symmetric spaces |
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