Noncommutative Riesz transforms - A probabilistic approach

M. Junge, T. Mei

Research output: Contribution to journalArticlepeer-review


For 2 ≤ p ≤ 8 we show the lower estimates ||A1/2x||p ≤ c(p) max{||F(x,x)1/2||p, ||F(x*, x*)1/2||p} for the Riesz transform associated to a semigroup (Tt) of completely positive maps on a von Neumann algebra with negative generator Tt = e-tA, and gradient form 2F(x, y) = Ax*y + x*Ay - A(x*y). Among other hypotheses we assume that F2 ≥ 0 and the existence of a Markov dilation for (Tt). As an application we provide new examples of quantum metric spaces for discrete groups with rapid decay. In this context a compactness condition follows from Sobolev embedding results based on a notion of dimension due to Varopoulos.

Original languageEnglish (US)
Pages (from-to)611-680
Number of pages70
JournalAmerican Journal of Mathematics
Issue number3
StatePublished - Jun 2010

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Noncommutative Riesz transforms - A probabilistic approach'. Together they form a unique fingerprint.

Cite this