This is an announcement for the paper "On the operator space UMD property for noncommutative Lp-spaces" by Magdalena Musat.
Abstract: 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<\infty, 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 \tau, then Lq(M,\tau) is OUMDp for 1<p,q<\infty.
Archive classification: Operator Algebras; Functional Analysis; Probability
Mathematics Subject Classification: 46L52, 47L25 (Primary) 60G46 (Secondary)
Remarks: 30 pages
The source file(s), OUMDLP.TEX: 120786 bytes, is(are) stored in gzipped form as 0501033.gz with size 33kb. The corresponding postcript file has gzipped size 135kb.
Submitted from: mmusat@math.ucsd.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.OA/0501033
or
http://arXiv.org/abs/math.OA/0501033
or by email in unzipped form by transmitting an empty message with subject line
uget 0501033
or in gzipped form by using subject line
get 0501033
to: math@arXiv.org.