Rosenthal's theorem for subspaces of noncommutative $L_p$
Junge, Marius ; Parcet, Javier
Duke Math. J., Tome 141 (2008) no. 1, p. 75-122 / Harvested from Project Euclid
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We show that a reflexive subspace of the predual of a von Neumann algebra embeds into a noncommutative $L_p$ -space for some $p>1$ . This is a noncommutative version of Rosenthal's result for commutative $L_p$ -spaces. Similarly for $1 \le q \lt 2$ , an infinite-dimensional subspace $X$ of a noncommutative $L_q$ -space either contains $\ell_q$ or embeds in $L_p$ for some $q \lt p \lt 2$ . The novelty in the noncommutative setting is a double-sided change of density
Publié le : 2008-01-15
Classification:  46L53,  46B25 
@article{1196794291,
     author = {Junge, Marius and Parcet, Javier},
     title = {Rosenthal's theorem for subspaces of noncommutative $L\_p$},
     journal = {Duke Math. J.},
     volume = {141},
     number = {1},
     year = {2008},
     pages = { 75-122},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1196794291}
}

Junge, Marius; Parcet, Javier. Rosenthal's theorem for subspaces of noncommutative $L_p$. Duke Math. J., Tome 141 (2008) no. 1, pp.  75-122. http://gdmltest.u-ga.fr/item/1196794291/