2005/01/03 by Magdalena Musat, Musat, Magdalena
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Holomorphic and Operator Theory #math.FA #math.OA #math.PR #msc:46L52 #msc:47L25 #msc:60G46
paper · pdf · doi:10.48550/arxiv.math/0501033
30 pages
arxiv created 2005/01/03 · arxiv updated 2009/12/01
We study the operator space UMD property, introduced by Pisier in the context of noncommutative vector-valued Lp-spaces. It is unknown whether the property is independent of p in this setting. We prove that for 1<p,q<∞, the Schatten q-classes Sq are OUMDp. The proof relies on properties of the Haagerup tensor product and complex interpolation. Using ultraproduct techniques, we extend this result to a large class of noncommutative Lq-spaces. Namely, we show that if M is a QWEP von Neumann algebra (i.e., a quotient of a C^*-algebra with Lance's weak expectation property) equipped with a normal, faithful tracial state τ, then Lq(M,τ) is OUMDp for 1<p,q<∞.